I think, firstly, that your proclaimed 'freedom from bias' might be argued by many here, given the editorial commentary that you've attached to some lines of the post - commentary such as '(last of course least lol) Constantinople' that is unwelcome and frankly unappreciated on this site.
In non-polemical discussion, the ancient patriarchates are ordinarily cited not by primacy, but by precedence (which is not necessarily the same thing).
As to St Andrew the First-Called, even the 1911 Catholic Encyclopedia (not a source for which we here have much enthusiasm) acknowledges that he preached "in Byzantium itself, where he appointed St. Stachys as its first bishop" - a pretty telling claim to his having founded the See.
I suggest that you might want to read
Who We AreMany years,
Neil