How long could Genoa realistically keep its Crimean colonies?

Once the Ottomans rise, it's game over. With the Ottomans controlling the straits, there is no way the Genoese can hold onto these territories. If the Ottomans' rise is stopped, I imagine these areas could be kept for longer - not that a strong Byzantium would be a much better bet. Sure, the Genoese might be allied with Constantinople for a while, but eventually there is bound to be conflict, and at that point the Crimean colonies can be easily cut off. I think the best bet would be a very disunited Balkan/Anatolian region, with a disintegrated rump Byzantine Empire that only holds on to Constantinople and some neighboring lands (like just before the Ottoman conquest), but Anatolia is also fragmented with various competing emirates. In this case, the Byzantines could have a long-term alliance or partnership of some sort with the Genoese that would help the latter supply their colony and the former to use its naval power to assist the enemies of the Byzantines (with Genoa expanding in the region much like Venice did IOTL). With a bit of luck, Genoa might even be able to hold onto these areas until the rise of nationalism (assuming it still happens) - at that point, due to general upheaval and the difficulty of protecting such a far-flung territory, I don't think it is possible to hold on any further.
 
To be honest, I think even sans the Straights being cut off, at some point in the 17th or 18th Centuries they're going to fall to either the Crimean Khanate or Russia.
 
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