An alternate path for your timeline could end up this way
Well, I am honestly toying with that idea, since I am also toying with a renewed Tetrarchy (after another age of crisis similar to the Third century), but that would not be the POD of my timeline. I was referring to a timeline where moving the capital was the actual POD ( during the Heraklians or as a consequence of the fall of Constantinople in 711)
The Sultanate of Rome: Hello there, I have the high ground.
At least the Seljuks had the decency of never claiming the imperial title (theirs was mostly a geographical one)
Frederick I of Sicily at Palermo: Am I a joke to you?
Yes!
More seriously I appreciate the guy for being a skilled and incredible ruler, still I refuse to call him (or anyone before and after him) a Roman emperor. So yeah, Palermo as the capital doesn't really count.
This was the basis for the anti-Latin sentiment leading to the massacre of the Latins in 1185.
Ironic, considering how later on you had some Romans claiming to be Latins, in order to enjoy the same privileges.
I mean while Trebizond is a very good trade city, the Komnenoi may actually move the capital to a more central location like say Sinope. For the purposes of this tl, I call it Trebizond so people know what I mean. But within the actual story, contemporaries would probably call it the lands of the Romans just like with Epirus in otl (the title of Despotate is pretty anachronous for this period).
If the Komnenians manage to conquer Nicea quickly, before the homonymous empire becomes a thing, they could even move their capital there and be know as the (ALT) Nicean empire. Or just Pontus would work fine as well. I think It's mostly a matter of how much land they end up with before the situation settles definitely. Is Sinope a more important city than Trebizond right now?
Bulgaria actually had alot more potential considering the internal discord of the Crusaders. If someone like Tsar Boril had taken over instead of Kaloyan in otl, its likely that the Bulgarians would have conquered the de-jure European lands. Of course Kaloyan was skirting the line between Catholicism and Orthodoxy so that would bring a number of theological issues.
Considering how romanized were the Bulgarians at this point in time, and more importantly Orthodox, they might actually have a shot at being remember as true claimant to the imperial throne. Just one that started playing the game way before 1204. Still rooting for the Komnenoi though.