Who were the "original Romans"? Is a 4th century Gallo-Roman an "original Roman"? Would he have been recognised as such by a Roman living a five hundred or a thousand years previously? Would the thousand-year Roman have recognised the five hundred-year Roman? When, exactly, does this leap from true Roman to mere Byzantine occur, in your view?
What you seem to be hitting on, here, is that culture changes and that identities change, but that they don't necessarily change in the same way, but this isn't a peculiarly Roman problem.
(edit: Also, and I mean this as an observation rather than a criticism, but do you not see a certain contradiction between your insistence that time and cultural divergence render peoples as objectively-distinct nations, while at the same time propounding a Jewish nationalism that takes as a premise the ability of shared descent to over-ride time and cultural divergence? It is not obvious that the identification of a tenth century Byzantine with Julius Caesar is no any more spurious than the identification of a twenty-first century Jew with, say, Maimonides.)