Now that there is 1355, there are important developments at the Black Sea. According to the Treaty of Milan, both the Genoese and the Venetians are barred for 3 years from Tana. However, the Genoese have the well fortified Kaffa so they are not seriously affected. The Genoese will use this reprieve and the internal instability of the Golden Horde to gradually establish a proper colonial empire around the Genoese Gazaria and achieve supremacy in the Black Sea. Since they lack Chios and Lesvos, the importance of the Black Sea trade is becoming even greater once again and at the same time the reliance on a friendly or at least neutral Syracuse, that controls both shores of the Messina Straight and the Ionians and Aegean Seas.
When the Genoese defeated Ioannis VI, one of the terms of the treaty they imposed was barring access of Greeks merchants to Tana. But who were those merchants? Considering the devastation of Thrace and the relative prosperity of Morea, my guess is that most of these merchants were Monemvasiots, who were already established in the region in a series of cities. Pegae included. At the same time, we know that merchants of Messina were active in Caffa during the 1280s and 1290s. My guess would be that gradually their operations would have shift to Tana, the open emporium. In OTL the Genoese were content to allow access to Tana to the Florentines who were important trade partners, so I would expect they will allow the Sicilians and Monemvasiots to trade there as well. Ι expect the Despotate to be the third more important player in the Black Sea after the Genoese and the Venetians. Basically to have the role of the OTL Tuscans.
Then there is the matter of
Pegae. The well-fortified town seems to have sheltered two groups: refugees from the rest of byzantine Asia Minor and a Monemvasiot mercantile community. Since I doubt that the town had an extensive hinterland, I would argue its character was more mercantile in nature. In OTL Monemvasiots of Pegae had received a lot of privileges by Andronikos II and III. The most important was the privilege of exkousseia, excemption of all taxes. Some historians like Ostrogorsky claim that exkousseia also provided judicial privileges, while Kalligas considers it entailed civic autonomy. Pegae remained freem from the Karasids and then the Ottomans until 1363. It seems to me, that Pegae must have been an autonomous city that paid tribute first to the Karasids and then the Ottomans, basically a coastal Philadelphia.
What is important is that basically all the population of Pegae would be more loyal to the Lascarids rather than Kantakouzenos or Palaiologos. And Thessaloniki provides a potent example. Moreover, it is a fair guess that the Despotate merchants, or at least the Monemvasiots would regularly use Pegae. Crossing the Dardanelles from the south is a very taxing process, especially for oared vessels, due to the very strong currents flowing south from the Black Sea. Pegae's location right after the straight is ideal for the sailors to rest and replenish their water supplies.
Lastly, there is the case of Heraclea Pontica. The city seems to have been left to its own devices til it was sold to the Genoese. While I don't know under which conditions it was sold, the nature of the genoese expansion in the Black Sea could give some indications. Usually the Genoese would capture a port and then they would buy it from its rulers.
Overall, it seems that there is a good chance that the Despotate has a sizeable footprint in the Straights and the Black Sea.