When I first encountered therianthropy (being a were), everyone naturally assumed reincarnation was the name of the game, so I kind of accepted it. But over the years I've come to find that I'm not really that spiritual and that belief in reincarnation is not necessary to justify therianthropy. I also don't believe in souls and stuff.
All that said and accepting that OP clearly stated that the theory has holes. I just wanted to point out -- this is not to prove or disprove anything, it's just a curious tidbit that I noticed:
For some reason, many therians seem to have a similar theory of reincarnation, that is not linked to the traditional belief of what reincarnation is or how it works. For example, the belief that us being therians means we were animals in our previous lives, is not compatible with a traditional view of reincarnation, where it is very unlikely if not impossible that someone who is born a human would have been an animal in their previous life.
This is because the traditional notion of reincarnation is based on a concept similar to karma, where what you are born as depends on the benefit to society you were in your previous life. However in the traditional view, animals are seen as driven entirely by instinct and therefore incapable of choosing to benefit society, and therefore making it impossible for them to accumulate enough karma to advance to being born as a human.
Longer thread discussing all of this in more depth:
The reason for this difference could be explained by simple american (most people on TG are from English-speaking countries) ignorance of traditional Asian spirituality. But whether you agree with this or not, it is curious that this "version of reincarnation" is so common among therians.
Perhaps it has something to do with how I encountered it as well, which is... that it's simply common among therians and passed between us as a kind of therian (sub)culture. Along with tails and now recently, masks and quads.