The two Latin states to the south are on the down-swing. Achaea is falling out of its glory days (and IOTL would be beaten severely by the Nicaeans), Athens isn't particularly in any danger but it isn't much on its own and it doesn't have the interests of Sicily behind it like Achaea did.
Epirus seems to have not been able to compete IOTL, see no reason for differences.
It seems the late 13th century was a time of opportunity for the Byzantines. It's a shame what happened in Asia Minor messed everything up. Oh Michael, you and your dynastic squabbles.
My bias, they need to revitalize their maritime and commercial sector. The whole thing of using cut glass in place of jewels in their ornaments is poignant, people with almost nothing but their dignity. But it is also pathetic, because these people were sitting on the friggin Golden Horn, like starving to death in Ft. Knox. Until the Ottomans boxed it in, there is no excuse for Constantinople not to be a great and rich port city, and the Greek seafaring population is plenty to man the merchant marine and war fleets.
With money, the Empire can mobilize its human resources when needed. It has roughly the population of Henry VII's England. The agricultural sector is inherently poorer, but if Constantinople can make up for that, they should be able to put a formidable army into the field in wartime, and have seapower to dominate the Eastern Med and the spice trade. They will take a hit from Portugal, but so did Venice. The empire is more balanced, because it does have an agricultural sector.
But all of this calls for a mind set like Venetians. The Byzantine political and intellectual elite historically did not necessarily disdain trade, but it wasn't much on their radar. But Venice itself had a lot of Byzantine heritage, so the latent potential may be there in the Byzantine mental toolkit.
The starting place for this sub-POD could be the Basileus realizing that he can't have Venetians and Genoese owning part of his country and all of his trade. Even more critically, he has to go back to the sequence of events from 1082 to 1204 and see that it is not enough to boot the Italians - Greeks have to take their place.
The natural temptation of OTL Byzantines, IIRC, was to buddy up to the Genoese against the Venetians, who were the bigger military threat. But that just puts them in hock to the Genoese. The bolder move would be to cut off the Genoese trade privileges in Constantinople, and grant those privileges to local merchants instead, in turn for some obligation to make their ships available in wartime.
This in time could set up a virtuous cycle of powerful Byzantine merchants, whose influence further pushes the government toward supporting trade. The system, however, might well be 'state capitalism' - as in Venice. In the 17th century this could potentially make Byzantium the Netherlands of the east, not as rich as the real Netherlands, but not poor.
A bit OTL, but my favorite Byzantine TL, which I've never seen explored, is a Norman dynasty. I think Guiscard would quickly have decided that Constantinople was worth more than a filioque clause and gone Orthodox, which basically makes him no longer a foreigner in the eyes of the people. Norman voltage and the 'two Sicilies' could be the basis for a resurgent Byzantium on considerably different lines than 'no Manzikert' TLs.
