You've got it backwards, of course. The Pope holds Peter's authority and office. You split off from the Catholic Church, not vice versa. Thus, in the analogy, Lincoln is like the Pope and Lee is like the orthodox patriarchs or Luther or pick your favorite schismatic.
None of the ancient sees established by the apostles survive unbroken to this day except for Rome, the ancient see of Peter. All the patriarchates are beneath Rome in terms of authority as any perusal of the first three hundred years of Church history easily shows.
You can claim what you like about Constantinople, but there is absolutely no theological reason to believe that Constantinople has any claim for authority that competes with Rome's. The closest you can get is to say that a Roman Emperor had his capitol city there for a time - that's not theology, that's just interesting cultural data.
Tha analogy still fails due to the fact that no other country in the world, and certainly not the USA, recognized the legitimacy of the CSA. However, nobody in their right mind would refuse to recognize the legitimacy of the Orthodox or Southern Baptist denominations as existing Christian denominations.
As for whether Orthodoxy split off from Roman Catholicism or vice versa, clearly the two sides disagree on that issue.
Your refusal to admit that the Pope is not the head of these other denominations is as nutty as if GWB refused to admit that Tony Blair is the Prime Minister of the UK.
None of the ancient sees established by the apostles survive unbroken to this day except for Rome, the ancient see of Peter. All the patriarchates are beneath Rome in terms of authority as any perusal of the first three hundred years of Church history easily shows.
The Orthodox Churches actually admit that, of the 5 patriarchs, Rome's is first among equals. However, the Orthodox Church simply does not admit that the Pope is the head of Christianity, and neither does any other Christian denomination.
Your claims fly in the face of reality.