I just came across an interesting tidbit from the Third Vatican Mythographer—which is stultifying for the most part, puts the "darkness" in the Dark Ages—but which occasionally preserves some valuable bit of lore that fell through the cracks. This is from 6.26, in the section on Pluto:
Thus the Egyptians, who are experienced in established wisdom, preserve bodies longer so that the soul might endure for a long time and be subject to the body, and that it might not pass over quickly to others.
Though one finds attestations in ancient authors of Egyptian belief in reincarnation, I don't recall another instance in which this is specifically connected with mummification, though I could be mistaken. This bit could also be an unacknowledged fragment of Seneca's lost book De situ et sacris Aegyptiorum, as the Third Mythographer quotes Seneca earlier (6.3).
Writers like Herodotus routinely claim that Egyptians believed in reincarnation. I see nothing wrong with the notion that Amenti is somewhat akin to the Tibetan Bardo, and that further births may well occur, that it's a matter in the operations of the resurrection literature of controlling the circumstances and ensuring the fullest faculties and resources for the resurrected self to choose their next life. Understand, however, that I can't support this with any evidence to speak of.