I suffered a massive brain failure when I made that edit about Silk, probably because I was already thinking ahead to a solution (which I doubt you'll like). But you can only trade for one Silk, which means you'd have to conquer the other two. That implies an invasion of the Far East. That seems awfully hard to pull off, especially since the time will be spent preparing for the Turks, dealing with the Turks, or recovering from dealing with the Turks. It would practically involve conquering China, and/or setting up colonies far outside your settlement area.
The idea I had would be kind of kludgey, but what about rejiggering one of the Corporations so that it becomes available early and used to secure Silk (and maybe other Far East) resources? It's not hard to do: I know practically nothing about modding, but I played around with the files and managed to recast Jewel Co. (renamed "Cathay Co.") so that it trades for Silk and Sugar and Spices, is founded by a Great Merchant, and becomes available with Guilds. I didn't go so far as to try changing its other properties (generating money and culture), but it might be weakened by stripping it of those properties. In that way, the Byzantines, by founding that company and getting in contact with the Far East civs, could act as a conduit, getting control of those extra resources and then trading them to the European civilizations.
NEXT DAY EDIT, TO AVOID DOUBLE POSTING:
I've played a couple of Monarch-level games up to 1400. My observations, fwtw:
1. There is some diplomacy bugginess, but nothing crippling to game play. I got TONS of "X has [done thing] to X" announcements. Countries declaring war on themselves; countries making peace with themselves; countries vassalizing to themselves. The Arabs do it, the Vikings do it, the Spanish and the French and the Portuguese do it. "Let's do it, let's go screw with ourselves." [/FakeColePorter]
2. The Arabs are easy to deal with. Hierousalem can be retaken and held with minimal fuss, and Cataphracts and Pikemen are sufficient for that job and for seeing off the initial Arab armies. After you've killed seven Camel Archers, two Swordsmen, and any Longbowmen or Spearmen who are foolish enough to wander nearby, the Arabs won't give you any problems, even if you remain technically at war with them.
3. Every time I whip temples/cathedrals, I lose at least one city to secession. But I can get two Cathedrals without much worry by 1100AD without whipping if I crank out missionaries and switch to Organized Religion (for production boost) and Serfdom (so your two Workers can rapidly bring mines and quarries into action.)
4. The tech race is also doable, if you concentrate on Meditation - Philosophy off the bat and then beeline Astronomy. (Beelining Astronomy is almost the same as beelining Chemistry, too.) Alexandria is a Great Scientist assembly line, and these can either pop useful techs or give you specialists and Academies.
5. I mentioned above my concern about the Silk condition. I myself love the idea, which is why I'm drawn to the idea of a modified corporation to handle it. Otherwise ... Um ... Change it to "Secure 1 Silk, 1 Sugar, and 1 Spice resource"? I don't know how the game could do a check, but "Open the Silk Road" by building a road between Constantinopolis and Beijing? Maybe have a treasury of a certain size by a certain date, so that the player would have to balance research with treasury growth, and make Great Merchant trade missions to the Far East?
6. Turk vs. Byzantine Spawn Action is hellacious, which is no surprise. Probably only the Babylonians get screwed harder by a spawn. You MUST kill them ASAP. Even then ... Well, I assume this is a feature of RFC, and maybe it's a new one, but even after I killed Sogut, the next turn I got a "flip" announcement, and for ten turns my units would bleed away to the north shore of the Black Sea, even though the Turks had no city. In one game they got Rasht in a flip from the Arabs; in another they had no cities, but weren't destroyed until I sent units up to crush their little band of defectors in the Crimea.
7. Oh, and because it must be said: "This mod is a lot of fun." I really like it.
8. Oops, one more observation: Maybe other people will be able to find a use for it, but I don't find the UP useful in the least. During the Middle Ages you're likely only at war with the Arabs, and if you deny them Hierousalem and the north African cities (which most players, they will not be a Mediterranean sea power. During all my games, I only built one galley in each game before exiting the Middle Ages, and that was to ferry missionaries/GPs from Athens to Alexandria.
A MUCH LATER EDIT: Just an update on the most recent game. As I anticipated, I got the Tech UHV without much problem. The Arabs finally pissed me off, and shortly after I smashed the Turks I used the army I'd created to dispatch Saladin. I took Cairo and Mecca, then made peace. Saladin lingered for a bit, and then collapsed. That was around 1400, I think. I didn't expand anymore, just played around. My stability gradually got worse and worse. I used the Taj Mahal Golden Age to make a change in civics that I hoped would shore up my empire, and started putting jails everywhere. But I lapsed back into Unstable.
And then in 1745, with no secessions to warn me, the Byzantine Empire collapsed in civil war. I kept Constantinopolis and Iconium, and that was all. The Turks got Trebizon and Alexandretta. The French (who had settled Tunis) got Tripoli. All the other cities (my originals plus Cairo and Mecca) went Independent. I guess I wasn't really surprised, except maybe that with the Greek stability map the empire managed to hang on as long as it did.