I counted on the Korean city having no more than two spears here on Emperor difficulty, and that stack was indeed enough.
After building a total of those two archers and three swordsmen, Madrid started on the Colossus while Barcelona supplied more military to fight against Korea.
Presently, the Ottomans threatened me for Iron Working. Since they couldn't possibly hurt me, I declined. They declared war. A few turns later, Japan did the same thing! But nothing happened in either war.
After my pair of curraghs had explored all that they could safely reach, I sent one on a suicide run. It survived two turns at sea and found the island of the Byzantines and Aztecs.
In the first picture above, you can see I'm researching Code of Laws at 100% rate. I executed the Code of Laws - Philosophy - free Republic jump easily.
Besides the Colossus, what other wonders would help? Not a whole lot, really. Barcelona built the Mausoleum of Mausollos because long-term happiness is always useful. (Barcelona got that wonder because Madrid, as the seaside Colossus commerce-producing city, was slated for Shakespeare's for the late game.) Madrid built the Great Library, but it only ever gave me about three techs.
My initial handful of military proved sufficient to hold off Korea for quite a longtime. The AI is still abysmally terrible at tactical maneuvering. I didn't even have catapults because I got Mathematics late, but I had two elite swordsmen that carved up everything that Korea offered, one unit at a time of course.
At this point, I revisited the info thread, and realized that there was to be no scoring in this epic. So, I decided to go not for a fast finish, but for a reliable outcome. When the objective is an early finish date, tech whoring is the rule of the game, to get the AIs to contribute anything they can to the global research pace. However, in this game, for once, I wouldn't do that. I was rapidly building a technology lead thanks to spending 100 turns as the only civ in Republic, and I wanted to see how long I could hold onto such a lead with only the two cities.
Still, though, it did take a little while to start researching into techs with something worthwhile to build. Both cities topped out at size 12 with 15-20 shield production quite quickly, and needed to spend the production on something. Madrid built the Great Lighthouse for a subtle reason: to enable trade routes with Japan over sea squares, so I could import luxuries and lower my luxury tax. Barcelona started accumulating shields for nothing in particular, and wound up with the Temple of Artemis for no good reason at all.
Well, the Temple did have one good reason: it started my Golden Age! That wouldn't have been hard to do later with Sistine or Bach's, but right now is indeed the optimum time.
During the Golden Age, I also built the Great Wall, for no other reason than it was a cheap 200-shield build to pull in wonder tourism. Tourism starts becoming significant around the 1500-year age mark for a wonder, and maxes out after 2250 years. So basically anything built before the BC-AD calendar change will pay off handsomely down the road.
In the Middle Ages, I beelined research to Astronomy with a prebuild ready to go for Copernicus in Madrid. (The Colossus is multiplicative with all the double-science-in-city wonders, of course. So is wonder tourism.) I also built the Sistine Chapel easily during the Golden Age.
I remained at war with Korea this whole time, with my small handful of elite swordsmen easily killing everything. I did build a couple horsemen, which ventured in and pillaged Korea's resources to reduce them to throwing archers at me. I didn't have any real material to gain in Korea's war, since we aren't allowed to build more cities, but I did make the very real gain of drastically and fatally stunting the growth of my on-continent neighbor.
With Astronomy came another opportunity I'd forgotten about: Conquistadors! I built two, that with stats of 3-2-2 all-terrain-as-roads, easily outclassed anything that resource-deprived Korea could put out and easily pillaged every square in the nation.
Economically, I maintained 100% research all the way through the middle ages. With Korea providing a steady stream of enslaved workers and settlers, I used all my native workers for population merging and gem colonies up north. I only had about 7-8 military units this whole time, which costed pocket change in unit support. I didn't need any luxury tax with the Sistine Chapel, Mausoleum, my own two luxuries, and two lux from Japan. My expenses were about 15 gold per turn in building support, and I made more than that from judicious tech sales, like this monopoly sale of Literature.
On about my 40th elite attack (see, I don't always get the luck there), a Great Leader finally appeared. Since it's impossible to get on the army-Heroic Epic path with only two cities, he really didn't have anything to do. He'd eventually just rush a factory.
I couldn't accept them, of course, but plenty of cities started trying to flip to me...
Towards the end of the middle ages, I irrigated Barcelona to +10 food production and started farming workers out of it for a little while in preparation for railroads. During the middle ages, I researched strictly required techs and skipped all the optionals.
The Ottomans picked another fight, but my conquistadors and a couple medieval infantry held off any shenanigans and peace came soon. The Byzantines also declared war after a refused tribute demand. I accepted the war-happiness boost for quite some time, and never saw a Byzantine unit before making peace.
In the above picture, Sun Tzu's is a prebuild for Newton's.
Then Nam'po finally managed to flip - not to me, but to the Ottomans!
I entered the Industrial Age in 970 AD. The most advanced AIs are Japan and Ottomans, and they lack Theology and Gunpowder. That's a lead of 10 technologies with only the two cities, if anyone's counting. Madrid is pulling in 260 science with the two science wonders stacked with the Colossus and growing wonder tourism income.