Well, pardon my ignorance in East European matters, but didn't the Ottomans precisely get in the Balkans as allies/mercenaries to the Byzantines to fight the Bulgarians? So if they aren't literally carried in Byzantine ships and then left to their business in Europe, wouldn't Constantinople probably fall way earlier, but to a powerful Bulgaria?
Interesting idea, actually.
What, I'm curious, would a Bulgaria that grabbed Constantinople actually look like? Its probably going to relocate its capital there, and its Tsars are probably going to start calling themselves "Roman Emperor" (as that is, after all, a more prestigious title than "Tsar of Bulgaria"). So, assuming Bulgaria survives, what are the chances that Greek gradually replaces Bulgarian as the language of culture/government, and the state turns into Byzantine Empire 2.0?
Or conversely, is it more likely Constantinople becomes Slavicized?