In my opinion, it's going to take a shift in Byzantine politics on the scale of the French Revolution to solve any of its issues.
In 1400, or thereabouts, Byzantium is an economic protectorate of Venice and a military protectorate of the Ottomans. There's some friction because it's a protectorate in a strategic position, so it has slightly more influence than, say, the Balkan satellites of the Ottoman Empire later had... but it has as much chance of defeating them as Skanderbeg or Vlad the Impaler (and quite possibly less).
If the Crusade of Varna succeeds, somehow, in actually beating the Ottomans, I would sooner see the Byzantines ending as Cyprus did; absorbed by Venice after some neat politicking. Although I suppose it might linger on as a position similar to an imperial free city (but then under Venetian suzerain) in Constantinople until either a Bulgarian, new Greek or Turkish state takes over.
Although, of course, there's always the insane-luck option of a Greek/Orthodox revolt rising up in Greece or so after a particularly nasty Ottoman defeat (either against Timur or the westerners, although in either case a single defeat might not even suffice), at the same time as Venice and Aragon are otherwise occupied. In that case, a lower-nobility/popular revolt might rise up, take over Greece-proper, and nominally recognize Byzantine overlordship while effectively usurping power from the decrepit institutions in Constantinople. Such a state would presumably somewhat distrust both the Italians (who've lost Greece to the Turks precisely because noone trusts them, it seems) and the high nobility, but even then any interruption in Venetian or Turkish distraction in the first 10-20 years will lead to the state quickly being returned to subservience.
After 20 years under an energetic reformist ruler (who, preferably, avoids assasination AND the temptation to become Emperor in name as well as practice) in the vein, perhaps, of Matyas Hunyadi, the state might have a chance to become an unequal ally rather than an outright protectorate. From there, it's a matter of luck and skill to hold on for a few more decades of serious reform, until it can finally return to being a power on a level where it can actually start removing the Venetians from the Aegean and the Turks from Asia Minor. Retaking Crete or Trabzon is going to take a century of continuous luck in both rulers and politics, and by the time it's succeeded it's as much the Byzantine Empire as the Byzantine Empire is the Roman Empire or Turkey the Ottoman Empire.