Actually, in my current 600 AD Spain game, Byzantium is alive in 1620. Not super stable, limited to two cities (Byzantium and Athens, of course), vassalized to the HRE, but still plugging along. HRE is so strong that I doubt the Ottomans, who are decently strong but well behind me and Germany, have the guts to declare war on Byzantium. So I don't really see Byzantium going anywhere soon, unless they're even less stable than they appear.
This is actually a very strange game, I think some elements might have been broken when I last updated. Most notably, the Thais never spawned, so the Khmer are going strong. Other interesting goings-on: the Mongols did well and collapsed quickly in the early 1400's, the Arabians have a decently large empire and were the first to Liberalism, but are suffering from instability and Ottoman pressure. They just lost Baghdad. The Germans crushed the Russians and took Sevastopol, Kiev, and Novgorod, so they're beastly. Italy actually managed to do something! They culture-flipped Rome immediately after the Germans took it, then France declared war on them. I was expecting France to roll, but to my amazement the Italians not only held them off but took Naples off their hands. Once they were at peace they offered to be my vassal, I had no choice but to accept

I missed the first UHV by 2 turns due to those darn Dutch, but things are going well otherwise so I think I'll play this one out.
Oh yeah, I've also been noticing some problems with city re-naming. It's pretty common for cities not to be renamed upon capture: for example, France briefly captured Florence, but when the Italians took it back it kept the French version of the name.