I feel that the discussion is stuck in the wrong set of terms and concepts, and I know of no religion or philosophy that meets the OP's specification.
Rebirth of some kind is almost always asserted by religion since without it an evolutionary view of consciousness becomes impossible as does any sensible system of ethics. The subtler idea is of an ocean of consciousness from which individual 'alters' arise like waves, not separate but identifiable as a disturbance.
Thus our consciousness would arise from the ocean and when it falls back it carries with it impressions or tendencies, and these will lead to a further incarnation of consciousness since it has yet to be fully purified of ego-desires and so forth.
This is the merry-go-round that Buddhists, Taoists, Sufis, Theosophists, Advaitans and their like are trying to get off for the sake of union with 'God' or 'nirvana' and eternal peace.
The common 'Christian' idea that our final reward will be to be resurrected in our human bodies is a non-starter. It is not taught by Jesus and it is not a goal pursued by any seeker with ambition. A body is a limit and not compatible with true freedom and immortality. Even if we were resurrected in this way we would still not have achieved our potential.
As for the numbers game, this is irrelevant once we think of consciousness as unified. For the mystic consciousness is All and it is ONE. It would be only our conceptual delusions that lead us to think otherwise.
I suggest leaving modern Christianity aside and having a look at the classical form of it, and also checking out 'rebirth' in Buddhism. You'll have objections but they probably won't be the same ones. It may also be worth reading Schrodinger's argument against the multiplicity of souls, an idea he rejects outright in favour of the Upanishadic view of consciousness, rebirth and God. This would the view taken by the Perennial philosophy in general and it is not easy to find telling objections to it. Indeed, it has proved impossible to date.
It is worth saying that even quite skilled Buddhists struggle with the details of rebirth. Also it can be noted that while Buddhist doctrine can be justified and proved in logic for the most part, the doctrine of karma and rebirth is, as far as I can tell, a 'lemma' in the sense that while it is logically coherent and consistent with the rest of the doctrine it cannot actually be proved in logic. That is, the ontology, epistemology and cosmology can be justified by metaphysical analysis, but not karma and rebirth. They would follow naturally but we are not forced to endorse them.
All in all it's a very difficult topic and only accessible to a serious student of comparative religion or hands-on yoga practice.