Presently at home, the Forbidden Palace now completed in Moscow to cut my distance upkeep by a good 20/turn, plus 30% inflation.
Here's a shot of the current demographics. That 90,000 figure for "worst rival population" was an important clue to finishing off Russia. 90,000 is the population of a single size-5 city, which told me that the one Russian city I could see was indeed their last city.
But more importantly, there's now a negative value in that GNP gauge. All those junk Russian cities sent my maintenance costs through the roof in all three facets - city distance, number of cities, and civic upkeep. I might have to win this game with a seriously crashed economy.
On the home front, Leader Four from my capital was an Artist at low odds who settled in Beshbalik anyway for the cash and Representation science. Leader Five was finally a Prophet (I'd hired priests with Angkor Wat) to go for the Taoist shrine.
With the Taoist shrine now in place, it was worthwhile to flood ex-Russia with Taoist missionaries. Organized Religion would help all the new cities get up to speed as positive economic producers rather than net drainers. Each city whipped a granary, theatre, and lighthouse (taking leverage, I confess, of the whipping bug whenever possible), then grew up to size.
After Guilds, I completed a beeline to Astronomy. Here's what the seriously skewed technology graph looks like now (plus Astronomy):
Yes, I've skipped Code of Laws and Civil Service, while going on to Gunpowder via Guilds, and Astronomy. Funny what a couple of variant rules can do to one's path through the tech tree. :) Code of Laws would come presently.
I started in on Japan while cleaning up the last of Russia. I'd already sent more than enough force in Russia's direction to finish off Peter, so my fresh troops went towards Nippon, including galleys to carry them.
This time I just miscounted, having one too few non-horse units in the stack. One of the axemen declared war on a white whale or something, and hopped back on the boat rather than fight the city. I took an extra turn so the two catapults could strip Tokyo's defenses, then captured the city with no losses.
I left the surplus axeman in Tokyo while advancing on Kyoto -- but Japan mustered a stack of four samurai that slipped past mine (like ninjas!) and recaptured the city. I re-recaptured it, losing one knight. (Incidentally, knights render Japan's UU ability irrelevant, with the immunity to first strikes.) I would then hold serve at Tokyo for a little while until I could get a fresh boatful of knights over from home.
And here's a current wide-angle overview shot.
Moscow is building Research -- yes this is a bit silly -- in order to preserve the overflow from a recent whip until the rest of the courthouses finish to qualify for the Forbidden Palace. Hey, that's an extra 20 hammers of head start on finishing the critical national wonder.
Ning-hsia is still cranking military at ludicrous speed -- here it's building an axeman in a single turn thanks to the Heroic Epic. It would build a few axeman to serve as cardboard-cutout military garrisons for ex-Russia, then return to training knights to trample Japan.
And eventually I did get to Kyoto with this stack, newly reinforced with three knights from home.
The catapults did get there a turn before that second wave of knights arrived, and used that turn to start bombarding. But I'd "sent" all the units at the target city at the same time, so I figured that was OK by the variant.
With Kyoto gone, that stack would take out the rest of Japan in short order without any other events of note.
BTW, I hate to quibble semantics, but I need to for a moment. Sirian wrote that to determine compliance with the variant rule, count your units when you send a force to a target city. Problem is, "send" is a loose concept. When in wars like this -- especially later on when chasing around the scattered islands -- I shuffle units around all the time based on counterattacks, defensive position, healing needs with medics, and so on. I might start a particular knight towards a particular city, then divert it to somewhere else like a pressing counterattack. Or I might see enemy borders adjust in a way I hadn't anticipated, allowing more units to be added to an attacking stack. Or a stack might just fail to take a target city, but I might have a boat in the area intended for something else, that can divert to bring in a couple amphibious attackers against my first target.
That said, I was certainly following the spirit of the variant rule. After burning a few surplus melee units on Japan, my actual offense was indeed 100% mounted units, with all the rest of the slots taken up by defense-stripping bombardment units and one longbowman or grenadier to defend against counterattacks. I hardly used suicide catapults. In fact, I reorganized most of my offensive stacks to include only two bombardment catapults (taking an extra turn to strip city defenses), since I had a hard time mustering one knight per catapult on most of these attacks. The catapults never died; the knights often had to trade with defending pikemen, requiring frequent replacement.
On the other front, my army that had conquered Russia consolidated, regrouped, and managed to remember not to declare war on a boatload of fresh knights from home. Now it was time to start on India, with this stack:
That stack captured Madras with the loss of only one suicide catapult. But then it pulled back onto that 75% defense hill, behind that Guerilla II longbowman. Three times I allowed India to recapture the city, while I healed on the hill (one knight was Medic) and lured in more foes. In this way, I could proactively pick my fights (the AI never counterattacked that longbow) and get the most mileage out of each suicide catapult while whittling down India's stacks.
When an additional boatload each of knights and catapults arrived from home, I finally captured the city for real.
However, at the next city, my force got seriously cut down. Two elephants and a pikeman burst out and killed three of my knights. I was forced to retreat these units to Madras yet again (fortunately India never had enough counterattackers to break through the knights and kill the catapults), until my home cities researched and built some grenadiers as bodyguards.
Presently at home, the Forbidden Palace now completed in Moscow to cut my distance upkeep by a good 20/turn, plus 30% inflation.
So after the Grenadiers beeline, my next research path was clearly to go straight to Military Tradition. This finally included Civil Service, which is the latest I've ever gotten that. Along the way I got Nationalism before anyone else, so naturally I went for the Taj Mahal thanks to the Marble captured from Russia.
And with yet more reinforcements from home (I was sending my entire military production at India now), I got to Bangalore with this army. It's neatly within the variant rules: seven knights, four catapults, and three grenadiers.
I lost one knight and one suicide catapult in the attack, so the survivors were free to go attack again.
In 1625 AD, Military Tradition came in and I started building cavalry. I also declared war on research for a few turns, for cash to upgrade the knights out on the front lines.
And here's the stack with which I got to Delhi. The only loss I took was the one suicide catapult, which I replaced with a Grenadier and continued marching to the next city. Unlike knights, cavalry are strong enough to have no fear of elephants or pikemen, so I didn't need suicide catapults anymore.
With the Indian conquest came several helpful wonders: the Great Lighthouse in Madras, the Great Library, Sistine Chapel and Parthenon (expired) in Delhi, and Notre Dame in Lahore. Delhi even got itself a free culture expansion thanks to Sistine Chapel + Great Library.
Well, OK, maybe Notre Dame wasn't so helpful. Nice move there, AI. 
So while that main stack conquered the Indian mainland, I put together this new stack from home to get started on the outlying islands.
Three cavalry, one grenadier, and two catapults meet the variant restrictions. Funnily enough, I think that my composition of this stack would've been exactly the same without the variant rule. I had two galleons available in the area, so six units was the total I'd be taking. Two Accuracy catapults will strip a city's defenses in two turns, three cavalry provide the offense, and one grenadier can provide forest-boosted defense in case of counterattacks.
Japan had been reduced to this one city out on a little sandbar. A frigate sailed there to keep watch on the city for any ships that might try to make a run for it (remembering that Require Complete Kills option.)
And that frigate discovered a very confused quartet of other rival units sharing that same sandbar. Both Qin and Cyrus had sent a settler pair that just sat there instead of settling. I have no idea what the AI was thinking.
With Chemistry, I also built numerous Frigates to patrol the seas. One galleon had sighted a stray Japanese caravel a while back. That boded ill, since that one Japanese refugee camp was still responsible for a good chunk of my war weariness. It slipped away, and I had to send about four caravels and frigates chasing all around the southern hemisphere to find it.
"J3." "Miss." "H6." "Miss." Finally my caravel lucked out and caught the Japanese caravel when it stopped to gaze at the icebergs. "I7." "You sunk my Caravel!"
Finally, one of my naval divisions did make it to Japan's last city and killed it. Thanks to that hunted-down caravel, that was indeed the last of the Japanese. My war-weary cities breathed a big sigh of relief as I was finally able to declare war on the culture tax.