Skipping over some detail, the important strategic point here was stopping research. After Code of Laws and slinging Philosophy and Theology, I researched nothing between 1100 BC up to a little ways before 1 AD. All the commerce went into cash rushing. Priority targets were granaries in new cities, workers everywhere, and theaters to enable Globe. Settlers got built with chops, since the Imp bonus doesn't apply to cash rushing.
The big priority was to keep all the legendary cities growing at all times - don't let them spend turns on workers and settlers if at all avoidable. And they must work nothing but cottages. Plains and hills got cottages too. With all the town-boosting civics working together, this was the right way to go. The Charismatic trait paid back pretty well here; the legendary cities were just about at the edge of the happy cap for a few dozen turns. Would have had to prioritize temples sooner without Cha. Environmentalism also helped a lot more than I would have guessed; Susa even managed to exceed the boosted health cap for a while, so would have been seriously retarded with -6 food lost to unhealth.
My goal was to have every legendary cottage planted and worked by 1 AD. I fell short by 8, two at Persepolis, two at Pasargadae, and four at Susa. But the Hanging Gardens was timed just right to boost Persepolis and Pasargadae up to their last cottage, the hardest pop point to grow. Not all these cottages were actually being worked by the legendary cities; Ecbatana, Tarsus, and Gordium each worked a cottage or two for their neighbors until the legendary cities grew enough to take them on for themselves.
I had only expanded to seven cities, but Ainu and Frankfurt should be dead meat for flips taking me to the usual total of nine. Gordium up north was mostly there to claim stone. Lacking Marble is painful for a culture game; Ecbatana is struggling there to build the National Epic, and I would end up skipping all of the Mausoleum, Sistine Chapel, and Taj Mahal.
Ecbatana in the south was my Great Artist farm. Not a super site, only +10 surplus food and it had to farm three flood plains to do even that. But that's enough, since without Caste System, a city can only have five artist slots anyway, two from the theater and three from Globe. It would put out only a total of six artists before the game ended.
India turned up with Aesthetics, which was my cue to turn research back on for the ten turns it took to reach Music. A little while later I went for Divine Right for the religion, but that would be the last tech I researched. The terminal techs of Philosophy, Music, and DR, and brokerages chaining from them, turned around in trade for the entire medieval era: Currency, Feudalism, Construction, Machinery, Civil Service, Paper, Guilds, Engineering, Banking, Compass. I didn't research a single one of those myself.
My religion plan worked to perfection. I had founded the four later ones myself, and the first three had each gone to different AIs, who all eventually sent me missionaries. Even the fastest culture game still wants all seven religions if it can get them; you do finish building all seven cathedrals before the game ends.
So I just kept cash rushing, cash rushing, cash rushing everything. I bought forges, missionaries, temples, spending 200 or more gold every turn. The cathedrals were correct to slow-build, because the various resource doublers don't apply to cash rushing. One interesting bit was the lack of Organized Religion, meaning monasteries were needed for the missionaries.
This lasted until T150 800 AD, when my intuition said it was time to change to culture slider instead. I quantified this some other time (can't find the reference, was probably some forum post but not at RB) and figured out that it's correct to stop cash rushing approximately when each legendary city has one or two cathedrals. Also at this time I hit the 1-man Golden Age with the second Prophet spawned from my Oracle/Stonehenge city, having waited until almost all the towns matured into the Universal Suffrage hammer.
In the wonder department... well, there wasn't much of a wonder department. I did build the Statue of Liberty in an off-legendary city, and Statue of Zeus with the ivory doubler just for the culture. But Sistine was entirely skippable with no state religion and very few specialists. Mausoleum was skippable with few Golden Ages (only had one). Didn't reach the tech for Taj Mahal until after it was built. No need for anything else like Sankore or Notre Dame. I got one late Great Engineer whose most useful function was to clock Versailles for a bit of culture, a move I've made a few times before in culture games.
One thing that didn't go according to plan was culture flips. 60 turns went by where I had cultural majorities in some adjacent cities, but no signs of a revolt. Eventually I gave up and crammed in two more cities of my own to get to nine.
Naturally, ten seconds after I did that, both flips finally came.
I don't think this was the intent of the civics-enabling techs, but Democracy turned into very lucrative trade bait. Mansa was researching very strongly and trading everything to me. I traded Democracy away for Constitution and Printing Press (not often you get to trade a tech for its own prerequisites!), and turned those around into brokerages for Gunpowder, Nationalism, Astronomy, and Constitution. That makes like twenty techs since my last actual research. I didn't really do anything with them though, aside from a very late Hermitage.
One more overview. If this report feels a bit perfunctory, it's because the game was too. I played fast and sloppy, didn't really optimize tile improvements for the new and flipped cities, or resource sales, or try to synchronize temples in sets of 3, or rigorously calculate when to switch from cash rushing to culture slider. Didn't precisely optimize the culture timing, and the cities went legendary 3 turns apart and Pasargadae missed shaving off one turn by less than 100 culture. (Clocking Versailles in this city instead would have saved the turn but I didn't calculate that far ahead.) There's not much interesting to say here; we all know how to build missionaries and temples and cathedrals while running the culture slider, and park on Wealth once everything is done. The legendaries maxed out between 1000 and 1300 culture/turn, about as high as you get without corporations.
The civics variant actually subtracted interest from the game. The only thing to do was work and grow cottages, without any thoughts of whipping or Caste or Mercantilism or when to switch out of Bureaucracy or trying to match AI favorite civics. I can appreciate variants that cut to the bone stripping out chunks of complexity (like Mach Five or Holiday Wishlist) but wouldn't want to play them all the time.
Got one more flipped city for a total of three. Nice, not often that you get to flip two wonders.
Culture Victory in 1470 AD, turn 207. Subtract Cyrus' 30-turn handicap and my score is 177.
That was actually kind of slower than I expected, compared to my record of 940 AD, and that without any cheaty goodies like these civics. But I guess for Cyrus with marginal traits and no relevant UU/UB, it's pretty good. I do think I went the right direction in the leader department; Financial isn't strong enough to do that 30 turns faster. The critical path isn't commerce (look how early I killed research), it's growing onto all the cottages and building all the cathedrals.
Thanks to Swiss Pauli for sponsoring.