And so now the plan was to beeline Industrialism and conquer the world. In the meantime, I'd finally build the Globe Theater so that my dozen garrison units could stop playing police. Also, once Industrialism came in, I would build watermills on all available tiles to replace towns, trading three commerce for two hammers on each such tile. I also built the Iron Works and Heroic Epic (the early barbs had given me a level 4 archer to qualify), getting London up to about 140 shields per turn for building military units.
Huayna and Alexander were both thoroughly Friendly, thanks to sharing both Confucianism and Hereditary Rule. But the logistics of conquest demanded I start with one of them, preferably Huayna as his financial GNP is starting to approach mine.
Now, I hate declaring war on Friendly AIs. I *very* much rely on Friendly rivals never attacking me, and I hate to backstab the system. Fortunately for my conscience, Huayna presently (surprisingly) changed to Christianity, and my plan was set in motion. I flipped Paper to Isabella for Theology. Also, now I didn't have to cling to Hereditary Rule for diplomatic reasons, and Representation offered much science with nine super-specialists in my city. So I now double-revolted to Representation - Theocracy.
While researching to Combustion (we do have Oil) and Industrialism, I built a set of four cannons, enough to remove a city's defenses in one turn with a couple Accuracy promotions. Industrialism finished in 1755 AD, and I went to upgrade all my old garrison warriors and archers thanks to the thousands of cash that had been produced by the Confucian shrine and settled specialists with Wall Street. But now I discovered that nothing upgrades to Marines. (Why not? I can understand the balance problems in allowing a mass upgrade to Tanks, but what's special about Marines?) The best I could do with all my cheap garrison units was to upgrade them to Infantry. Whatever; Tanks are going to be the core of my offense anyway.
And in 1765 AD, I declared war on Huayna. I'd been hoping to have my tanks steamroll musketmen, but he had gotten Rifling. Tanks actually don't have the advantage against riflemen fortified behind a strong city defense. My tanks had to proceed with deliberation, making sure to wait for the cannon stack to remove each city's defenses first.
I went shopping for alliances, but religious differences kept almost everybody from liking me enough to help. Alex was the only aid available to buy, for some outdated tech. He was actually pretty helpful; when my tanks got to the Incan capital, he was there with a stack of catapults and had softened it up nicely for me.
After the Tank beeline, the next research was Plastics for the hydro plant (London didn't have the hammers to make tanks every turn, so this would help.) Then I went for Military Tradition for West Point. First time I've ever meaningfully built that national wonder; it sure turned out helpful here, allowing City Raider 3 tanks right out of the gate with the barracks and Theocracy.
So the tanks steamrolled over Inca, wiping them out in 1836 AD. Here's the stat of the day:
Subtracting out the early barbarian fights, my kill count in the Incan war was 102 to 5. 
Twenty to one is the ratio. Still, with my unit production rate at less than one per turn, and well more than twenty future enemy cities on the map, I would need to sustain that kind of kill ratio for quite some time in order to actually pull off the conquest win.
After the Incan war finished, Spain would be next for logistical reasons. On the "clock" of the Inland Sea map, the Inca had been between 10:00 and 12:00, with Spain occupying the space from 12:00 to about 1:30.
Just to boost our relations even a bit more, I signed Defensive Pact with Alexander for the few turns between the wars while healing and positioning. But that came up big!
One turn before I would have declared war on Spain, she declared on me instead! And that pulled Alex into the war on my side, for free!
Spain had never been in any wars, so I got the full brunt of all the fresh but obsolete units that Isabella had wandering around...
Yeah. That's a kill ratio of 22 to 2 in a single turn, with my megastack playing defense rather than offense. At that kind of odds, this isn't going to take long. Twenty turns to eliminate Spain, to be precise.
My kill ratio in the Spanish war was 147 to 6. Even better than in the previous war, now that more of the tanks were better promoted.
While blasting Spain with the tanks, I beelined to Robotics next. London built a Machine Gun every turn for about twelve turns, to save them for an instant mass upgrade to Mechanized Infantry. I still had thousands of surplus cash, and prebuilding cheap units for mass upgrade was the only way to convert that cash into military usefulness.
I also slipped in two Destroyers to take control of the sea; one to protect the home fish from getting pillaged (losing the harbor-boosted health would be a headache), and the other to kill convoys and bombard coastal cities. I'd later add a Battleship as well. The AIs had lots of frigates and galleons floating around for target practice; the Destroyers reached Combat 3 and 4, and the Battleship was Combat 3. Yes, a Combat 3 Battleship just unquestionedly _owns_ the waves.
So with Spain destroyed, the next target on the Clock of Doom was Japan. However, there's a bit of a problem here:
How did THAT happen? Tokugawa signed a Defensive Pact with Monty?! 
Well, the stars and planets aligned just right for those two leaders to build good relations. They shared Buddhism as well as common-enemy bonus from when they both fought Germany. And Monty's tech path had him in Mercantilism for quite some time, which just happens to be Tokugawa's favorite civic. Thanks to having a trading buddy, Tokugawa had even pushed into the tech lead besides myself.
And let's not forget that the power graph still looks like this, with Monty and Tokugawa combined commanding about four times my power:
So how do I deal with this? I'd really prefer not to take on both civs at the same time. Especially since Alex has turned chicken on me:
While I was deciding what to do about this, Winamp's random selection brought on this song. You can't listen to that without feeling spurred on to action. 
So I declared war on Tokugawa, and let Monty join in. Well, the Defensive Pact breaks when one of the parties declares war (I hadn't quite realized how that works). So Alex would join in with me now; only against Montezuma, not both, but that's good enough for me. As long as somebody besides me is eating the initial brunt of Monty's stacks.
BTW, this picture shows where Greece is technologically -- no Education, while I'm at the doorstep of mechs!
So I'm stuck eating the initial brunt of Japan's stacks, which are large and advanced enough to actually hurt mine. Tokugawa was still two techs away from infantry, but I'd forgotten about SAM infantry, which he had and which are tougher than rifles. A pile of SAM infantry plus some junk units takes out my cannon stack!
So my tank stack (13 strong now) has to pause on killing cities. I have to build some replacement siege, which would be cannons that got upgraded to artillery right away when I researched that tech. I also built a transport to deliver the new artillery over to the front line. Japan's a higher priority to attack than the Aztecs right now, because Tokugawa is ahead of the Aztecs on GNP and tech but behind in power. Pick the softer fruit first, or something like that.
I'm not ignoring the Aztecs entirely, though. That stack of 11 upgraded mechs goes south through Greece to hold off and clean up Aztec units, and take out a couple fringe cities. Eventually that stack tries to push through to a coastal Aztec city -- no artillery required here because my destroyers had done the bombarding -- but gets swarmed by cavalry. Five of the mechs actually die, and the rest have to retreat to a hill to heal.
Now here, I ended up pulling the AI's puppet strings a bit. The AI would not ever counterattack that mech stack on the 75% defense tile in neutral territory. (In fact, the AI hardly ever seems to counterattack in neutral territory in general.) So I would sit the mechs on that hill to heal, then advance them two squares southeast onto that forest. Unlike tanks, mechs do get terrain defense bonuses, and one of those mechs had even been promoted to Woodsman II. Every time the mechs advanced to that forest, the AI would immediately slam all units in range against the stack, but would be unable to kill my 64-strength (!) defender. Then the mechs could retreat again and heal in peace. In this way, that stack of mechs killed about 40 more Aztec cavalry and cannons without taking further losses. Finally, that stack received a load of four mechs by boat to reinforce, and razed that city.
On the research front, I was beelining Composites of course. But then I realized we had a serious flaw in the Modern Armor plan -- London had no aluminum! And no way was I gifting Greece up to the tech to sell me some, since I did have to conquer him eventually too. So I abandoned that line of thought, and went for Flight instead, then Medicine for some health at my city.
And now a worrisome realization dawned on me. I was now racing against time, to complete the conquest before my opponents could get more modern military units. I could handle riflemen and SAM infantry okay. But regular infantry (which have a built-in +25% bonus against gunpowder units, including mechs) would inflict significantly more losses on my attackers, as would machine guns. Tanks I could probably deny by hitting the resources, but I'd be sunk if anyone else got to mechs. There's no way mech-on-mech combat can maintain the 10-to-1 kill ratio that I'd need to avoid falling behind.
So I resumed plowing through Japanese cities, after taking a boatload of first mechs and then artillery over to reinforce that tank stack. I only built one transport, but it kept itself quite busy in ferrying fresh troops from my city to my city-killing stacks.
Tokugawa and Monty both still lacked Assembly Line despite having had all the prerequisites for some time. I kept hoping they wouldn't come up with Infantry anytime soon. Alex was still way down at Steam Power and Physics.
Presently, Alex made peace with Monty. He did his job, though, to blunt Monty's full stacks away from me. And now he would agree to alliance against Japan instead, so we did that.
This is the first time I've used either tanks or mechs; I've never before played a war with units more modern than infantry. I have to say that mechs are far superior. The chief advantage of tanks is that they can get City Raider promotions, but a mech with its higher base strength does just fine with Combat 2 + Pinch. The blitz ability of tanks is rarely relevant, since when attacking even at 90% odds, a tank usually takes enough damage that a second attack is unwise. However, the March ability of mechs is awesome. Check out this stack:
That army of mechs had just razed a city on yellow circle. They would all now heal right away this same turn, and heal again while moving to purple dot. With a medic in the stack, that's a total of 35% healing in two turns, all while moving. So all but two of the mechs would be fully healed and would raze Chinook only two turns after razing the previous city. By not wasting idle time healing, the mechs can march through cities twice as fast as tanks can -- and a mixed stack means the tanks get left behind healing while the mechs blitz onward.
Also, tanks' inability to get defensive bonuses is more annoying than one might think. Several times I've had to leave a tank uncovered on defense, and two or three enemy cavalry have come along to kill it. Mechs can cover tanks, but tanks' inability to get March means they're often left behind healing while the mechs are blitzing along. Finally, mechs, being gunpowder units, don't have a glaring vulnerability to counterattacking gunships. Mech Infantry are the axemen of the modern age.
I also built a stack of 4 gunships (actually upgraded from cheaper cavalry that were built just before researching Flight) to try them out, since I never had yet. This was a mistake. Gunships aren't strong enough to have a real impact on combat other than their specialized role of killing enemy tanks. They're good at pillaging if covered by stronger units on defense, but that's about it. I did promote one to Sentry which was mildly useful for the visibility.
I was also playing with different sets of promotions for the tanks. The units were starting at 10 XP with barracks + Theocracy + West Point, high enough to make the promotion game seriously interesting. Remembering Kylearan's story of his Drill IV riflemen, I promoted a few tanks to Drill III and then Drill IV, but I really wasn't impressed with their performance. You'd think a tank with 3-6 first strikes would be unstoppable (especially with Blitz), but taking those promotions meant that the tank couldn't take the actual strength-increasing promotions of Combat or Pinch or City Raider, and more often than not didn't actually have a significant strength advantage over the defender. Finally, the Drill tanks would run into the defender-selection bug where a defender with many first strikes is selected over an actually stronger defender (mech), and most of the Drill tanks ended up dying to counterattacks.
One Drill IV tank did survive all the way through, and ended as my leading unit with 62 XP. The rest of my tanks went about half-and-half for City Raider promotions or just generalist promotions of Combat and Pinch. Strangely, the City Raider tanks kept dying more often, while most of the generalist tanks survived. I think that's because the CR tanks were usually first in against the stiffer defenders, while the generalist tanks cleaned up the leftovers.
I also had fun with one Barrage III tank that survived long enough to tack on some City Raider promotions as well. Non-suicidal artillery, gotta love that. Especially on the occasions where it took little damage in winning its fight, allowing it to blitz again with a second collateral attack.
So by 1933 AD, Monty is gassed, and it's just a matter of mopping up the last few cities. Right? Er...
Where did Monty get all that?! And how did he sit on them without flinging them at me haphazardly? He baited me into that trap hook, line, and sinker, complete with a half-dozen cannons in the area too. Between turns, my stack LOST to the counterattackers. Twelve mechs lost to about thirty cavalry counterattacks. The RNG handed Monty withdrawals on more than half the cavalry attacks, too.
Well, I realize that the right thing to do now is not to attempt to rebuild that stack immediately, but instead to fall back through Greek territory in a stalemate while sending the next batch of mechs by boat to reinforce the army that's still killing Japan.
After Medicine, it dawned on me that research was now superfluous. The best thing available on the tech tree is Refrigeration for the plus to naval movement. But now I finally realize that I should be in Universal Suffrage, both for the extra hammers and for the cash rushing, so I start 5 turns of research on Democracy. (It sure won't hurt to inflict a little Emancipation anger on the other civs, either.) And Free Market is doing me no good since Alex is in Mercantilism (I have no trade routes at all), so I may as well go to Environmentalism. The extra health now let London grow from size 17 to 20, and an occasional cash-rushed mech meant London could keep rolling over the overflow so as not to miss any turns building mechs while not working the mines.
Monty and Alex somehow signed Open Borders, despite having just been at war only a few turns ago. And Monty having Open Borders access through Greek territory was giving me some logistical headaches in managing my tactical moves and counterattacks there. So this was my first occasion ever to make use of a "Stop Trading With" diplomatic request.
However, that didn't actually cancel their Open Borders. I'm afraid I don't understand why. Every time that I've complied with an AI asking me to stop trading with somebody, the Open Borders has gone along with whatever resource deals...
And Japan finally goes down in, appropriately enough, 1944 AD -- actually not by my hand but by Alex's.
And with Japan dead, Alex's status of "we have enough on our hands" is finally freed up for me to buy him in against Monty one last time.
The war with Monty followed the now-familar formula: keep the artillery marching to remove the city defenses, with the mech stacks attacking bombed-out cities. Coastal cities could be bombarded by the navy instead of waiting for the artillery (I had total naval domination with three Combat III ships). Monty was now truly gassed, especially with Greece back on my side.
I ran into some oddness here with the behavior of cultural borders after city razes. For some reason, when I razed Aztec cities, the borders did not disappear right away, but instead shrank at just one tile per turn. Here's an example:
Where's the city? Why does Monty get to temporarily keep cultural control over all those tiles when I've razed all the cities in the area?
Anyway, now there was one. It's down to me and Alex remaining, and he still lacks Constitution, Physics, and Combustion. So he's got cannons and rifles, but he's two techs away from artillery, three from infantry or SAM infantry, and six away from tanks.
And so with a heavy heart, I reluctantly informed Alex that this world wasn't big enough for both of us. I found myself wishing a Permanent Alliance was available so that I could take credit for the win along with my best buddy here. But that was not to be.
The final war took exactly 10 turns. Since I no longer needed to care about the unit kill ratio, I just marched the mechs up to the cities right away without waiting for any artillery bombardment.
Conquest Victory in 1973 AD.
The final military count (minus a half-dozen mechs that I'd lost against Greece):
The statistics:
My final kill total, including early barbarians and discounting non-combat units, was 756 to 67. Yes, it takes maintaining a kill ratio of about ten to one for the whole game in order to win OCC conquest. And that in turn requires a sizable window of tech advantage; you won't get that with axemen vs archers or knights vs longbows. As Sirian has observed, the economic vector really is overloaded in Civ 4. Economic supremacy translates into just about any other kind of supremacy that you want. The way to win an OCC conquest is not truly through military, but through economy until the military is a foregone conclusion.
Don't be fooled by my apparently fast-declining GNP. I stayed at 100% research with over 600 beakers per turn the entire game. The GNP graph dropped because my cash income dwindled from a high of +80/turn down to almost zero at the end of the game, thanks to both unit costs and to razing Confucian cities thus shortchanging the shrine. But that was 'fake' GNP that couldn't be leveraged towards research anyway.
And here's the power graph with a few annotations.
I didn't realize until I saw this screen that I only built the two great wonders, plus the shrine. It seemed like my city was continually constructing wonders for quite some time, but that was all the national wonders - Oxford, Wall Street, Iron Works, Globe Theatre, Hermitage, West Point. Most of the great wonders have civ-wide per-city effects that just don't help in an OCC. The only two wonders with a really good payoff for an OCC are the two shown right here.
Game score 5683 -- scoring even underneath my Adventure 14 *loss*. The other three lowest-scoring wins on that list were all OCC space victories. Anyone else think the game needs a score adjustment for the One-City Challenge? 
Fun game - thanks Sooooo for posting it. I'm glad for the chance to go down the conquest road in an OCC, and now I don't ever have to do it again. :)