AND I GOT IT!
Holy mother of pearl. I got the Silk UHV.
It figures that the game where I finally planned for every contingency was the game where everything came together so perfectly I almost didn't need to lay in any contingencies.
The biggest stroke of luck game early on, with the "Dutch" stability hit. That is the one thing that really needs to be fixed, btw. Sometimes it will sock you for thirty points, and sometimes ... Well, this time I'm not even sure it hit me for five. At turn 40, when I am often 15 points underwater, I was only showing -3. So I didn't have to worry about secessions until the Turkish spawn.
War with the Arabs also went well. Luck was with me there, too, in that Sana'a stood off a ways from Salalah, so that I didn't find myself squeezed in at the straits by hostile Independents on either side. That gave me a clear shot at the Indian Ocean.
I got Astronomy by 1260 by skipping Gunpowder, and upgraded my six Galleys to Galleons. I had two Settlers, two Pikemen, and two Workers ready to go, in case I needed to found two cities, and I sent them both out anyway, even though an early Caravel had found Hanseong still standing and still Independent. It was only lightly defended, but I still sent out my three Cataphracts and three Catapults, because I had no idea if it would still be Independent when I arrived. Not long after I set out, it and the other Far Eastern civs were hit by plague. It never spread, but it did kill off all the defenders. My little armada had to stand off outside Chinese/Japanese borders (which closed Hanseong off) because I couldn't get Open Borders with either one; and, besides, I wasn't going to occupy Hanseong until the plague had died out.
Diplomacy with the Chinese was ... odd. They were annoyed at me because of my heathen religion, but shortly after contact they offered to vassalize to me. That would have gotten me Silk and open borders for sure, but I decided to turn them down, because it seemed like an an odd one-off, and I wanted to see if I could get the Silk condition without vassalizing the Middle Kingdom. I did secure Silk from them, though.
In the meantime, the Turks had spawned, which sent my stabilitiy to hell. As soon as I hit Unstable I emptied my cities of their units, and loaded up most of them on the two Galleons I had still in the Mediterranean/Red Sea. I then staged a revolution so as to provoke a collapse, and changed 3 civics just to make sure that there would be two turns of anarchy. Again, remarkably, the collapse went off almost perfectly, and I lost only one Cataphract that I couldn't get away from Hierousalem in time. During the subsequent collapse/anarchy a barbarian Camel Archer captured and sacked Tripolis, which was actually a bit of a relief: I never liked that city. I then cruised the oceans, dropping units into empty Independents; only Cairo and Mecca had to be taken by land, and so within two turns I had my post-Turkish empire back again.
The loss of Mecca had cut my trade link with China, and when I re-established it I found out I had become their worst enemy. So I staged another revolution and switched to No State religion. (Yeah, while still running Organized Religion. I guess I must be High Church Unitarian or something.) By the next turn Qin was Pleased with me and traded one of his two Silk to me, and opened his borders. With that in hand, I moved on Hanseong and occupied it.
Another huge stroke of luck: Many turns before, I was about to pop a Great Person in Constantinopolis. I remembered TDK's suggestion that a Great Artist might be useful, so just before the pop I switched all my specialists to artists. I did it only so I wouldn't forget to after the pop. But even though there was only about a 4% chance of getting a GA on the next turn ... that's what I got. So I had a Great Artist in my baggage train when I arrived in Hanseong. His masterpiece ended disorder instantly and lashed the Silk tile down nicely. As it happens, it was unworked, so I had to bring up my two workers to put a plantation in. When it was done, I sent them back down and put up a plantation in the Philippines next to the city that I had just founded.
Result: Three Silk in 1410. The Victory screen confirms that I met the second condition. (And a relief it is, too, that the game doesn't check in 1450 itself, or the wait would have been agonizing.)
Now I just need to see if I can get the third UHV with my diminished empire. I've had to lower my research rate to 30%.
* * * * *
On a separate note, two bugs to report with the latest version of Byzantines_610, which I downloaded today. First, the game isn't checking for the Cathedral UHV. I built the second cathedral in 1090, and the demographics page confirms that I have 2 cathedrals, but the victory screen in 1410 still says "Not yet" next to that condition.
Second, I did a quick play as the Arabs, just to see what the other side looked like. By turn 10, Alexander was the leader of the Byzantines.
Also, fwiw, the Byzantines are ridiculously easy to defeat when you play as the Arabs, as you might expect given the size of the army you've started them with. I captured Hierousalem, Alexandretta, Iconium, Trebizon, Hesperides, and Tripolis pretty easily, though I did lose 3 or 4 Camel Archers. That pushed the Byzantines into Unstable, and I captured Alexandria when it seceded. Shortly after that, the Byzantines collapsed, as you might expect.
In practice, the Byzantines only come under threat from the AI Arabs in the first few turns, from the seven or eight Camel Archers, two Swordmen, and three Longbowmen that are positioned near Hierousalem. All the others head east to take Shiraz and the other independent Persian cities. My strategy involved pushing the Arabs hard in the early part of the game, so I don't know what they would do with the rest of their army if you let them be. But I think you could probably limit them to eight Camel Archers (the ones near Hierousalem) without making them any less of a threat to a human Byzantine player. This would also make the human-Arab game much less of a cakewalk.
But then again, where does Philippine silk come in?) If anything, India should have a silk:
