This is a fascinating thread for a lot of reasons.
I guess one question is where/how does consciousness arise or what specifically is it physically attached/related to during a lifetime.
This is the most important question regarding the matter.
My personal beliefs aside, there are currently 2 main opposing hypotheses in the scientific community regarding the origin and nature of consciousness.
The classical idea is that consciousness is stored in the tissues of the brain, or that it's generated by the electrical impulses running through the nerves.
In contrast, the hypothesis of "quantum consciousness" states in no uncertain terms that there is no scientific foundation for a belief that consciousness is contained within matter or generated through a biochemical process, but rather that consciousness exists independently of matter, somewhere out there beyond space/time as an extra-spacial entity.
That's a horrible oversimplification of both hypotheses, I know. OP, you should definitely read up on both of those ideas. Lots to think about. At least Google it for a quick summary because there's a whole lot of jargon to sift through.
As far as the idea of the atoms of one body being assimilated by a different body being considered "reincarnation"- well, that's definitely a different idea than what most people mean when they think of reincarnation.
However, if you believe that consciousness is ephemeral and perishes with the body upon death, then your proposed idea makes as much sense as anything else, including Steve Dougson's well-worded toilet paper analogy earlier in the thread. If that were the case, it would not matter matter if you were reconstituted as a shark, a tree, toilets paper, or all three at once, you wouldn't be aware of it.
On the other hand, if you believe that consciousness is permanently attached to or generated by the atoms that comprise your physical body, then Steve Dougson's analogy stands as a reasonable direct contradiction to that idea.
Transversely, if you believe that consciousness exists independently of the physical body and/or the atoms that comprise it, then regardless of which living things assimilate the atoms of your dead body, the consciousness will continue unaltered on a different plane of existence. Meaning the sharks, and trees, and rolls of toilet paper that have assimilated pieces of your corpse would clearly not be you either.