For the UHV:
in all the nations two of the victories were something the nation managed to accomplish (arguably depending on how you count 500 or 5000 culture points). Then one UHV is always something that the nation failed.
Greeks: First in philosophy, drama etc, they did build the wonders, but while they were strong in the Mediterranean Sea, they never went beyond. Hence they need to start the age of exploration by going around the world.
Romans: They did have the territory and all large Roman cities had the buildings, but Romans fell to the Barbarian Hordes.
Spain: Conquistadors = control of Inca and Aztec land, they were the first to settle in America, but soon other European nations joined the colonization and got ahead of Spain. So Spain should not let that happen.
The Byzantines were the most cultured in the early middle ages and Justinian had the the entire Mediterranean coast (he owned the sea). So:
1. Make Constantinople the most cultured city in year X is accurate.
Second condition would deal with the Byzantene domination in the Mediterranean. Conquer at least Rome, Egypt is fine too. Spain would be a problem because of Spain. So leave it at control Egypt, Carthage and Rome, or simply control 80 - 90% of the Mediterranean cities by year X. (it would be OK if spain has 1 - 2 cities as long as Byzantines control the vast majority of it)
Third condition: Where did the Byzantines fail, they lost Constantinople to the Crusaders and later they were overrun by the Ottomans. Make the goal as: Don't lose control over the Bosporus until 1600.
That is my opinion of course.