We may need to come up with a new system beyond Re:^n.
The "separation" between consciousnesses needs explanation. What is this separation? Why are they necessarily separate? Every time you wake up, aren't you a new consciousness with old memories?
The concept of the machine we're discussing implies that the body is reconstructed exactly as it was, even with neurons in mid-fire and your lungs filled to the same volume. Walking out, you can finish a sentence or a breath.
Give up the attachment to "life" and "death." The argument redefines them. Let's say someone operates the teleporter for you, but turns it off before you get reassembled, and leaves with your information on his bazillionbyte flash drive. Are you dead? Are you imprisoned? Is this so different from the principles of cryogenic freezing? Maybe doctors or insurance providers would describe you as "in stasis resulting from a lack of physical substance."
(These are the workings of a Ray Bradbury meets John Grisham novel. Henceforth I'll be referring to law school as "research for my book.")
Problem: After rejecting the argument "existence is better than non-existence, thus a perfect being (God) must necessarily exist," we've concluded that a description of something does not qualify as its existence. So how does a description of a man held on a flashdrive constitute his continued existence? To address this new technology, we have to abandon our old assumptions. Phenomenology: in all of your relationships, with family, doctors, passersby, they don't deal with you. They deal with a description of you, an image drawn by their senses. Do you do any better for yourself? Do I still have that mole on my back? Can I say so for certain without having to check? The teleporter accounts for the mole even when I don't.
Your assertion that identity is bonded to historical context: I swear to you, I saw that coming. I started to address it in my last post, and then deleted it.
If Lincoln's identity is historical, what if all record of him is lost forever? Does he exist less? Lincoln represents a part of U.S. history. What do you represent? To whom do you represent it? I don't think this branch of your argument gels with the rest. It sounds like you're trying to find an exterior locus of identity in other people, those who know or remember you. That won't convince spontaneous-Lincoln that he's not who he thinks he is. Identity is just a mechanism, like you described before. Identity is a word for representing yourself to yourself.
Problem of social identity. What do I have to do to encounter the historical Lincoln? If I see his body in the casket, have I "just missed him?" If I witnessed his birth, was he not yet the man he will become? If I see any 5 of the total 17 past members of Scorpions, does society validate the identity of the band?
Artificial needs a new definition in this context because the teleporter builds you a new body. The machine builds an organic body (teleportation). Artificial or not? An organic machine builds an organic body (birth). Artificial or not? Replace all of your organic body with inorganic components, one piece at a time. Is silicon-based Dan an artificial intelligence or not?
Is a beaver dam less artificial than the Hoover dam?