Maybe reincarnation isn't about mysterious soul units floating about waiting for a new body to enter.
Maybe it's more about a kind of generic consciousness/subjective awareness which persists and is a fundamental feature of objective reality, and finds subjective 'outlets' in brains. Consciousness could be a continuous and analog phenomenon at bottom, not discrete or partitioned. The partitioning would only come into effect when organisms become complex enough to receive it, like a radio receiving electromagnetic waves and converting them into sound.
When you think about it, there are no felt 'gaps' during life, since even during sleep and anesthesia, the actual experience is a kind of jump from an earlier point in time to a later point in time. You weren't experiencing the nothingness of the time interval.
Since experience of nothingness at death is impossible, or at least incoherent (since nothingness cannot be experienced), it isn't obviously nonsensical to suppose that our subjective consciousness will get transferred via a sort of jump to another being which is coming into existence at the same time as we die.
Because this new being will have a completely different brain and genome, all our old memories and experiences will be gone, but the subjective awareness would continue uninterrupted.
This could be compatible with a naturalistic view of the universe, since all it requires is that subjective awareness is in some sense an objective feature of a universe. And there need be nothing obviously immaterial or religious about subjective awareness. Even it turns out to be a sub-quantum mechanical phenomenon which requires a new psychophysical paradigm, it would still fit into a universe which obeys physical laws and operates in a rationally comprehensible way.
I'm not saying I believe this, just putting it forward as an interesting idea to consider.
There was an influential essay written about it, by tom Clark:
https://www.naturalism.org/philosophy/death/death-nothingness-and-subjectivity
