Looking more closely at the sittuation of Byzantium... No wonder they're in such a bad state! The emperor has managed to get one of the worst reputations I've ever seen in CK, so all his vassals hate him... From my own knowledge of the game, I'd say his position was pretty much untenable now, as that bad rep is going to haunt his hiers like a bad smell for several generations yet. My advice to the prospective Byzantines out there would be to play one of the princes (Vidin is next in line to inherit I think, and has decent stats), and either wait for the emperor to die naturally, or send him some less natural help.
As far as the Crusade for Byzantium, Georgia is too close, and too weak, to participate considering the current balance of power around the Black Sea littoral. i.e., the Seljuks would eat me alive.
EDIT: Of course, I intend to change that balance of power, but that's gonna take time...
fasquardon