This is the first of what will be a multi-edited post on the Byzantine game I'm playing. I'm not necessarily going for a UHV, just trying to see how long I can survive, and if Byzantium is correctly balanced.
Currently, I'm at 740AD, and I have a couple observations to make:
1.) These production, research, and growth penalties are really insane. I'd rather see my cities start smaller, with fewer movable units, no tile improvements, etc, and slightly reduced penalties, along the lines of what was done to France. I know the game is designed to engender a historically accurate demise of Byzantium, but let's not forget that, under Justinian and Belisarius, the Empire regained most of Italy and even southern Spain. I'd rather see a civilization that is more dynamic: capable of building up great strength, and surviving into the late game, especially if it manages to garner friendly relations with civs like Bulgaria and the Rus. Maybe a couple more early plagues, and some even stronger barb assaults could balance this. Further balancing a stronger Byzantium could be a true Turkish juggernaut. Let's face it: Basil the Bulgar Slayer killed off that civilization before 1050AD. The Byzantine Empire fell because of the "Terrible Turks", and a wayward fourth Crusade. Let's see the Turks have enough firepower to make it to Vienna, and let's see the Empire be strong enough to offer a formidable obstacle.
2.) Could Alexandria be considered "the core of the Empire"? Having it secede is really annoying, especially since, again, in the early part of this mod, Byzantium reconquered almost all of north africa. Honestly, I'd rather lose Sinope, Aleppo, Antioch, Tarsus and Ceasaria to revolt than Alexandria - and it was just as "Greek" as any of those cities.
EDIT 1: N.B. - If one of the ideas of gimping the Empire is to prevent wonder-building, I don't think that's really working. Maybe instead start the Byzantines with as few techs as possible, and just move wonders back in general. I basically always see the shrine of uppsala in Constantinople: Maybe push it back, and give Constantinople a bit more production, to remove the desparate need for the shrine?
Also, I think you might want to lower the foreign stability penalties for the Byzantines. They were surrounded by enemies on all sides for basically their entire history (see: relations with the "allied" Rus for examples), but the military, us-against-them mentality of the self styled "Roman Empire" helped forge a _more_ stable society in the face of adversity. To counteract this (and all the other power/stability enhancing features I'm proposing) make the quick-fix slow stability decay permanent - but only for Byzantium or, at least, ramp it up for Byzantium.
EDIT 2:
Minor Note: Cataphracts are wonderfully useful, especially if you can get them out before the Arabs get guisarmes (not hard to do). They were, however, the backbone of the Byzantine Army for most of its history. Maybe give them one more strength and take away one or both first strikes, encouraging the player to build them almost exclusively, and better reflect the theme system's army composition. Or, simply leave them as they are, and like Conquistadors in RFC, let them fortify.
Major Note: Well, with stability as it is, I basically can't have revolution in 900 AD without losing Antioch. But I don't think this is necessarily bad. As 3Miro noted, internal instability was a part of Byzantium's decline. I'd say, _increase_ the penalty for switching civics as the Byzantines, but start them with the actual civics of the empire (or a decent approximation), at least in three sections. I'm thinking Divine Monarchy, State Religion, and Religious Law(?). These should fit ell with Serfdom/Free Peasantry (which they had in practice depends on who you ask), Guilds/Mercantilism, and Vassalage/Imperialism.
Re: Wonders
Build order for Constantinople: Shrine of Uppsala, Monastery of Cluny, Workboat, Marco Polo's Embassy. Epheseus also built the Round Church: It's not yet 1000AD. It's not unbalancing the game, since Constantinople has no production, techs take forever to research, and the wonders have taken 500 years to build in Constantinople. But I'd rather get fewer wonders, and still be able to survive. Again, Constantinople definitely needs more production, if it doesn't always get Uppsala. Like another hill and copper/stone/marble (plains hills). Maybe fix the then lack of food by changing the fish to a clam and a crab. In that case, the other mineral could just be two plains-hills with forests, and change the wheat for barley. I'm not trying to just make Constantinople "totally l33t" - I just want to keep the food the same, but increase the production. Even if production penalties are decreased. Make Bureaucracy more viable for a nation famous for it.
EDIT 3: I just lost my first UHV condition, i.e. - make Constantinople the most cultured and populous city in the world by 1000AD. I'm pretty certain that I won on size with 14 (building a settler, though), and lost on culture. To be clear, My build order for Constantinople was Shrine of Uppsala, Monastery of Cluny, Workboat, Marco Polo's Embassy, smokehouse. That's all I had time to complete in 500 years. Now, it's fair to say that I could have built a hippodrome in there and won my UHV, or even could've just built culture. That said, I feel like it's unfair for a Byzantine player to be forced to go: Shrine, Monastery, Hippodrome, Workboat, MPE, Culture _every_ time, just to out-culture Rome. Especially since, in this version of the game, I haven't spent a single turn in anarchy. Possible solutions: Rome needs less culture, Constantinople needs more production as noted before (more buildings, more freedom), Byzantine production penalties need to be lowered. I'd recommend the latter two in conjuction, since they'll also fix other Byzantine problems.
Furthermore, I am playing on Monarch, so we can basically consider completing any of the UHV conditions impossible on Emperor (I'm assuming ramping it up would force Constantinople to also pitch in on building defenders.)