As I had planned, Tyrana did indeed get Sistine's:
But it was close, much closer than I would have liked. Orleans cascaded to and built Leo's on the SAME TURN. That's right, I won the race by virtue of the player's production cycle taking place before the AI's production cycle (or at least I think that's how it works). In any case, it was much too close for comfort. After all, Orleans could swap to Leo's if it lost the race - Tyrana would have had to swap to wealth! By the way, here's what Orleans looked like a turn earlier, I reloaded back from my autosave to take a look at just how close it really was:
AI mismanagement alert! For such a lousy city though, they certainly made it close. Of course, that's because Orleans started out working on the Temple of Artemis in BC times, and ended up getting Leo's. Even a weak city can build a wonder if the cascade remains alive long enough (in fact, slow-building cities are often one of the largest dangers when trying to manage the wonder cascade). Oh, and by the way, again all France had to do to win the wonder race was mine that mountain tile (or even that desert tile!) But the AI just doesn't know how to manage its cities, and so I once again fleeced the AI and walked away with another very powerful wonder. I've gotten Pyramids, Sun Tzu, and Sistine, all without prebuilding, which I think is a very strong showing.
Now, more importantly, what happened to the cascade once I took Sistine and France took Leo's? Well, for starters, most civs lost all of their accumulated shields and got nothing, but there was also large cascade to Copernicus and Bach's. With Copernicus a mortal lock for Tarsus in 2 turns, the one question remaining was over Bach's. I had already started it in Hattusas, but the AI civs had a huge lead on me, since they had been prebuilding for Bach's ever since Sistine appeared and I had to wait until Music Theory came on the scene to start it. Investigations proved that I could not overcome the AI lead, not even with my various worker tricks, since Madrid had become a production monster (finally, with semi-decent management) and would get the wonder long before I could. So I killed the shields built up in Hattusas and resolved to lose out on Bach's. Still, I did nail Copernicus in Tarsus, which damaged the cascade further and ensured that it would end when Spain built Bach's.
Tarsus therefore finished its 3rd wonder in 900AD. It's been nothing less than amazing for me, I may have gotten a huge break from that goody hut settler, but at least I made good use of it! Also, now that I have these wonders, I can stop running my absurd 50% luxuries for WLTKD purposes and get back to doing some research myself. Now that the cascade is mostly dead, I was free to start pulling ahead on science again (rather than deliberately slowing the tech pace to get more wonders), and my primary goal that I was driving towards was Navigation and Magellan's, which I knew would trip a golden age for my Commerical and Expansionist Hittites. Since I don't plan on ever fighting, this would likely be the only chance to get a golden age, and I wasn't going to pass it up. Naviagation was discovered in 940AD, and Tyrana (which was also a coastal city) began work on Magellan's, due in 16 turns at a slight food deficit. Madrid built Bach's in 980AD, as I knew it would from investigation, killing the cascade and leaving the rest of the wonders mine for the taking.
Just before taking this picture, Caesar had popped up and offered to swap world maps with me, which I gladly accepted. That explains why I can see stuff on the other continent. My civ is still building away; those new sword symbols for barracks are a riot when you have Sun Tzu's. Every city has one! Notice also the massive cultural pressure on the Iroquois city in the west (which never flipped, as I explained earlier) and the French army at "Fort Bayonne", as Joanie obviously wasn't taking any chances, not that I was going to attack anyone. As far as research, I'm driving now for Economics and Smith's, which will be yet another extremely powerful wonder for my civilization. Everything looking good, just another 10 turns to my golden age (and no one has even started Magellan's yet, so it's completely safe). On the other continent, Iroquois and Babylon are fighting a war in which Hiawatha is getting messed up; this is likely due to Babylon building the Statue of Zeus with its ivory. Up to this point, that was the only AI-AI war that had taken place.
I discovered Economics in 1060AD and Hattusas started in on Smith's; I don't know what techs the AI civs had, but no wonders were in production at all, so I was completely safe there too. Babylon and Iroquois signed peace on this date too, and the world went back to its usual state of peaceful development. Kind of surprising things haven't been more hairy on that other continent with Shaka and Caesar and Hammurabi (all high aggression) around. Everything still peaceful over on my continent.
As expected, Magellan sets off a golden age, which will allow my civ to blow past the AI and establish a strangehold on the tech lead from which I will never look back. At this point I'm now driving for Theory of Gravity and Newton's, which I want to make sure I get in Tarsus for the double-wonder effect. I will then go back and clean up the Democracy/Free Artistry optional techs, since the AI frequently ignores those. Except - here in this game, they didn't! I get pop-ups that the AI started Shakespeare's in 1160AD. At this point, I don't even have Printing Press, so I'm going to lose that wonder as well. Now if I could prebuild, I could easily get the wonder, but since I can't start it until I get Free Artistry, and that will take a minimum of 12 turns - no chance. Maybe this is simply a different feature of the Conquests AI, because I'm used to the standard and Play the World AI, where Free Artistry often didn't get researched until well into the Industrial Age. Here, the AI has ignored Newton's and beelined for Shakespeare, when I was planning on the opposite taking place! Well, chalk up a mistake for me. In my defense though, I couldn't see what techs the AI had (or trade for them!), so it is perhaps forgiveable. Madrid, that most hated city, would eventually get Shakespeare's. I would naturally clean up all of the Industrial and later wonders.
So I've lost out on Shakespeare's, which is bad in terms of style points, but otherwise doesn't really have much of an effect on my game. And while the AI civs have been off researching la la land techs like Priting Press and Free Artistry, I'm using my golden age to get into the Industrial Age and start into Steam Power and Industrialization. Now which do you think is a smarter move? 
Industrial Age achieved in 1255AD, could have done it much faster if I hadn't slowed myself down so much in the Middle Ages to get key wonders. Thanks to the golden age commerce, I actually was able to get Steam Power in 4 turns, which was surprising. Sid told me that I was "moderately advanced" though since I lacked those useless optional techs, ha! Shows how the AI "evaluates" how advanced you are.
Steam Power was discovered in 1275AD, the same turn as my golden age ended. I was horribly scared for a moment that I lacked coal - then found some on a mountain to the north near my tundra cities. Whew, that really had me worried. France had coal literally one tile across my border to the east, leaving me kicking myself for not expanding one city-site further. Of course I couldn't see the coal at the time though, and they could... All my jungle in the west had no coal in it. None. Well I wasn't expecting that... Rome not only had two sources of coal, but had two cities that qualified for the Iron Works! Zulus, Babylon, and Iroquis all had no coal, which looked to cement their status as non-entities for the rest of the game.
Industrialization followed in 1300AD, and a massive factory-building program was inititated across the Hittite lands. From there, I headed for Electricity, Scientific Method, and then Replaceable Parts - why not go there first for double speed workers and rubber if you have your choice of what to research? That just doesn't happen very often when you're playing on the higher levels, heh. I did my usual strategy of cash-rushing a factory and then a coal plant on successive turns in Hattusas then having it start on Suffrage; no need to allow even a glimmer of the cascade if I can avoid it. Turns still flying along with no need to check diplomacy, just concentrating on having my little guys workin' on the railroad.
Replaceable Parts are researched in 1350AD, and I make a discovery that's going to change my game incontrovertibly from here on out:
I have no rubber. None. Largest civ on the planet, half again as big as the #2 civ, massive tracts of jungle claimed in the west, and no rubber. Nada. Without rubber, I cannot launch the spaceship. I can't ask to trade for it from the AI in this game. Leaving aside all the units I can't build without rubber, I need it to win the game, so I HAVE to secure a source for myself. There is a source... two or three tiles outside my border in France. Just outside it. In that same jungle spot where the coal is. 
All I have to do is expand one more miserable city to the east and I don't have this problem. But I couldn't see the rubber there, and I delayed my expansion in order to get the Pyramids in Tarsus, after which the French beat me to that spot (again, since they knew there was rubber and coal there!) And ever since the very first turn of the game, when I sent my first scout west, I've been thinking in terms of westward expansion, not eastward. That has dictated the entire course of this game in ways I didn't understand when I started playing, with the result that I now must go to war in order to get my rubber source, all because I unconsciously made the decision not to push east.
You only truly understand a lot of things when looking back in retrospect. Life is like that too. 
I have two choices here. I can declare war on France and grab that rubber source to my east, which would be the easier action to take. But Joanie has been a consistent friend throughout the game (not like that tramp Isabella), and I just can't attack someone who has been such a staunch ally of me and given me a number of good trades. Furthermore, I have a ROP with France; when my galleys were exploring the French coastline, Joanie asked me to leave her territory or sign a ROP, and so I happily signed the ROP to improve relations. I just couldn't bring myself to attack my good friend Joanie and take away one of her core cities.
Fortunately, there's another option. Spain has no rubber (haha, dooming Izzy to perpetual weakness!) but Babylon does have rubber, and it's right across the coast from my cities. I have it circled on the map above (I also have my sole coal source circled as well). I've never made any kind of deal with Hammurabi, and I don't feel bad at all about taking it to him. So that becomes the goal for the immediate future, securing my own source of rubber across the narrow sea to the west. Now remember, I don't want to declare war; once that happens, the game could spiral rapidly out of my control, since I can't affect diplomacy in any way. In fact, I rather think this is where some of the less-experienced players may get into trouble in this Epic, not realizing that once you get into a war, there may very well be no way to get out of it! But I have no choice, that rubber must be mine.
It's time to toss the dice, and how they'll land is anyone's guess.
