AbsintheRed
Deity
but expansion right before the Mongols seems...like a bad idea. There is no time to get up some walls in the new cities, so they'll be overrun (unless you defend them with lots of knights) anyway. The UHV-date of 1250 helps here as most of the Mongols appear after that...
But if there is a reseach-goal after an expansion-goal for Byzantium it always means giving up some of the weaker cities to hasten your research.
And expanding around the Black Sea before 1300 means you probably have to fight one of the weakest civs in the game (Kiev) and you'll increase the difficulty level for Moscow.
A human Kiev-player will probably get one or two declarations of war from Byzantium, which could just take the fun of their game completely (since they usually vassalize Bulgaria).
Thats why I feel a new 3rd UHV that is conquest-based would be better than increasing UHV2s difficulty.
In your suggested game, I'd just settle all the "black sea"-provinces the turn before the time limit, then gift them away (Bulgaria, Kiev, France, Genoa). And then it's again "next turn, next turn" untill the tech is researched. I might even try to get 1-2 GEs to rushbuild the wonder, just in case.
Agreed, expansion is better fitting for the 3rd UHV
This way we also keep the 2 historical (semi-historical) + 1 ahistorical (unachieved) UHV pattern