Well, Byzantium has to defeat the Ottomans (requires careful playing for the first few years) and will pretty much get a free ride in Turkey after that, but will come up against Venice in the Balkans and the Mamelukes (and later Granada) in North Africa and the Middle East, and in any case doesnt have Arabic culture.
I do think that the culture rule I proposed oh so long ago would work well here, perhaps limiting it to cultures in Europe and West Asia. As it stands some culture monpolies exist (e.g. Granada with Arabic... giving it to Byzantium right off the bat would make the latter a bit too powerful) and nobody has Anglosaxon or (except Denmark) Scandinavian. If we wanted more conflict we could introduce some rule whereby owning a province of or having a land border with a culture gave you that culture after some time (so e.g. Byzantium could get Arabic, Scotland/Brittany could get Anglosaxon, TO could get Scandinavian...)
I do think that the culture rule I proposed oh so long ago would work well here, perhaps limiting it to cultures in Europe and West Asia. As it stands some culture monpolies exist (e.g. Granada with Arabic... giving it to Byzantium right off the bat would make the latter a bit too powerful) and nobody has Anglosaxon or (except Denmark) Scandinavian. If we wanted more conflict we could introduce some rule whereby owning a province of or having a land border with a culture gave you that culture after some time (so e.g. Byzantium could get Arabic, Scotland/Brittany could get Anglosaxon, TO could get Scandinavian...)