Definitely do this, Rome, while a shadow of it's imperial self, was still one of the most politically and religiously important cities in western civilization. I'd say that the city itself deserves a wonder version of the old St. Peter's Basilica.
Also, as far as the balance problems with Byzantium, I'd say that their late era situation is pretty historical (though I still think we need a Latin Empire faction in the late era only). They usually recover some of their old terrotory, especially Constantinople, but lose Epirus and Trebizond. Honestly, the late era turks do incredibly well until turn 25-35 when the Mongols unstoppably conquer the eastern third of the map. I realize that the Mongols did conquer most of the middle east and modern Russia, but we have no way of simulating the collapse of their empire and the power vacume that allowed new and powerful islamic nations to form, so I reccomend simply not giving them the power to never lose a single battle.
As for the early era Byzantines, they are overpowered, but the fact is that they were arguably the most powerful nation within the bounds of the map in 1100. The difference is that the AI (usually) cannot be powerful and at peace, and that the early turkish roster is very poor, and that we dont really have an equivalent nation to replace Bulgaria in the north (early era hungary is kindof a joke). The turks should probably be given some additional starting units, especially horse archers, and the balkan rebel settlements should be stacked to make them hard to capture.