the funniest part about the "TRUE ROMAN SVCCESSOR" state thing is that the country that probably has the best "legal" claim to the title also 100% does not claim it, don't mention it, don't even pretend it was ever a factor.
It's Spain.
Andreas Palaiologos bequeathed the titled to Felipe and Isabella of Castille. Although that remains contingent on Charles VIII of France's purchase of the title being invalid (I would argue so, seeing as he failed to live up to the stipulation of the sale)
The Turks invited the Ecumenical Patriarch of Constantinople over to make it official, so if you're one of those "The pope appoints the Emperor" guys then sure.