Let us be clear: There is an ethnicity, 'Hellene', living in geographical Greece, and an ethnicity (which is also a language), 'Latin', living in geographical Italy. Nobody claims that Hellenes are Latins; that would be absurd. However, there is additionally a citizenship, a set of rights and duties, which in the Greek is referred to as 'Romaioi'. To be a Roman citizen requires no claim of blood, although descent is the most common way to acquire it. Citizenship may be extended to anyone found worthy of the honour, whatever his ethnicity, religion, or station. So: Neither Hellenes nor Lombards are Latins; however, most Hellenes (not all, in that a few are unfortunately under infidel rule) are Romaioi, while very few Lombards are Romaioi. Further, the legitimate Senate of Rome currently has its seat in Constantinople. The existence of Roman citizenship cannot be expunged while the state survives in any form; accidents of geography are quite irrelevant. If the infidel were tomorrow to lay siege to Constantinople, and God were to see fit to punish the Roman people for its sins and cause them to be driven forth, and they sailed south to the very tip of Africa and there established a city, then they would still be the true Rome, and they would still be citizens, provided that their God-given rights and duties were not changed. Rome is not a place; it is an idea and an ideal. The saying, "An Emperor who does not hold Rome is only another rebel," does not refute this; it describes the realities of secular power within the Roman state, which has nothing to do with who is a Roman citizen.
As for 'Sublime Porte', you'll observe that the term is French and not Turkic. It refers, in my usage and not the hypothetical-anachronistic usage of some future that might have been possible in 1066 but has now been definitely averted, to Constantinople's position as the gate between Europe and Asia, and also the gate between the Mediterranean and Black Seas.