Does it not rely heavily on the concept of reincarnation working simultaneously with technology? The theory is that you can inhabit many different physical bodies. Why not a copy of the same physical looking you? The only onus would be the ability of the new body to actually function correctly in it's new state. Obviously it is instantaneous evolution and not one that takes years, which also introduces a less favorable body each time it evolves although the changes are less noticeable than a totally new copy would in a couple of seconds or minutes.
The question would be is it possible to mechanically make a copy that works, not necessarily would you be free to jump ship during the process. Most would say you do not have a choice in reincarnation. Those who claim there is only the physical you are stuck with the point it would not work period. There is not a function that would cause it to work, even if a perfectly working body was the result. You cannot transfer memories can you?
We point to stored states of "data" and say, "Sure, we can exchange the vary same state of data from one physical host and exactly replicate it in another physical host." What we do not know yet, would be is that still the same you, or another person entirely strapped with your memories. Reincarnation stresses the same you, but different memories. Teleportation may not be the same you, just a set of memories, that used to belong to you, but you ceased to exist.
If you are just your memories then reincarnation would not work because the biological means to make an exact copy of the physical storage space would not work, nor would it be logical possible for you to fit in a physically different physical host without changing some aspect of who you are. Not that you cannot evolve, but there is no guarantee that evolution would be for the better or for the worse.
Replicating states of brain matter is more complicated than simple states of a computer chip obviously. Even if we could force human memories or states into an animal's physical makup, what benifit would it be other than the collection of useless data that would have no relevance to the body of said animal. The same could be said about a new copy of a similar or even different humanoid body. As just data, it could present useless data, that the new physical body is forced to endure, and you still may not be you. If you are just senseless data, even in the same body, you could change from being you to something or someone else that is no longer you as well.