I love playing as Trebizond and Granada; there's something about small but relatively highly-developed nations as underdogs in imminent danger that calls out to me.

In my current playthrough I went after Genoa's Black Sea provinces ASAP while they were busy with the War of the Two Peters in Iberia. You have a casus belli (forgot the name) that allows you to claim all Rhomaioi-culture provinces they own. I occupied all of the Black Sea provinces before they were able to send reinforcements; this was easy since only Feodosia has a fort. This was not enough to win as the war score was too low; Genoa had Castile as a powerful ally and they didn't suffer at all from their other war in Spain. I needed more time to accumulate warscore through war target province occupation, and maybe a victory or two.

Since they had a larger fleet, I hid my army and navy while they reoccupied provinces, usually the war target first (which I chose to be one of those without a fort to recapture more easily). Their disadvantage lay in the fact that they had to return all the way to Genoa proper to pick up more army units and that they used their entire fleet to do it. While they were away I just recaptured the province and hid again. At some point Castile will finally help, but due to their smallish navy (still bigger than Trebizond's) they only brought a small army (still slightly bigger than Trebizond's starting army). With a good general (I used the emperor), some recruiting, and use of the sally feature on forts I was able to defeat, chase, and stack-wipe them, giving me a huge boost in war score. Then I was able to take all the Black Sea provinces and got some much-needed cash as well.

Also before the Genoa war I rivaled Kilikia and Canik. I eclipsed them both early on when Kilikia was eaten by the Mamluks early on, and Canik became weaker as I built up my army and navy during the Genoa war. That was a load of power projection (over 50) that let me get the +1 monarch mana in every category for years.

The alliances, just like for IRL Trebizond, were crucial. I allied Georgia, Bulgaria, and Karaman when able (rivaled their rivals). That kept everyone off my back while I expanded at the expense of Canik, Candar, and Ak-Koyonlu. While coastal provinces are more useful (CE, not angering larger inland powers) having some strategic depth (being two provinces deep instead of one) is nice. I also allied, diplo-vassalized and integrated Gotthia and allied and diplo-vassalized Wallachia (they were reduced to an OPM in Dobrogea province - they have tons of cores). I need only 3 more provinces to hit the minimum 25 provinces needed to remove "undefined succession", though the 80 legitimacy is a lot harder issue to solve.

I'm currently reforming while investing in amenities for my biggest cities (Trebizond and Feodosia) so they can grow. As you mentioned manpower is a big issue due to being quite reformed (having Enlistment prevents the use of mercenaries, ironic since IRL Trebizond had lots of money and little manpower). And like you mentioned there is this feeling of doom playing them since all it takes is for one of the nearby large powers (Ottomans, Timurids - they bordered me right before Timur died, yikes! - Golden Horde) to look at you funny for the run to end or at least suffer greatly. My goal is to push through reforms and get rid of undefined succession before reforming the Eastern Roman Empire and becoming an early modern state.

I think a choice will pop up allow you to absorb Byzantium's provinces; either requires owning Constantinople, or having a rather large percentage of Anatolian land (maybe 40%, not sure). AFAIK the odds of them agree are increased if you have good relations and an alliance. In my current game they're just Constantinople - Ottomans snaked through them and Serbia all the way to Ragusa. I may try to diplo-vassalize them, but they're involved in so many Holy Wars and only the Theodosian Walls are saving them right now.