Speaking personally, it was the suffering I’ve experienced in this life and the desire to free myself of it, not anything related to future lives, that got me practicing Buddhism. The reason I’ve stuck with Buddhism is because I found that my experience aligned with what the Buddha taught about dukkha, it’s origin, and how to stop it. In general, why people become Buddhist and start practicing is very personal and unique to the individual. However, whatever the specific reasons are, I think one should base their decision to accept Buddhism on trying out the teachings and seeing them work in their own minds. Trying to first validate a concept like rebirth, and only then start practicing, probably won’t lead anywhere. I don’t know if either Martin or tuvok consider themselves Buddhist yet, or have begun a regular meditation practice. If they haven’t started meditating and cultivating mindfulness, I’d say start there, see if you agree with what the Buddha taught, then come back to the idea of rebirth later.
The EBT (Early Buddhist Teachings) crowd probably aren’t going to go into deep, complicated philosophical discussions about the mechanics of rebirth. Avoiding that kind of thing is one of the hallmarks of the EBT. So you might not get your answers here. Trying to find parallels in biology or physics isn’t going to lead to satisfactory results, either, I think. I’m a big fan of science, but in the end whatever parallel someone claims to have found will be handwavey at best. Tibetan Buddhism has mountains of texts discussing very subtle philosophical points related to consciousness and rebirth. The Mind/Consciousness Only School (Yogacara), which was very influential in later Mahayana and tantra, developed a complex model of consciousness with 7 layers, and claims to understand how things like kamma are passed from one life to another. Buddhist tantra carried the idea even further. The Tibetans continue to study all of this. So, you can check out what they have to say. It will probably take a couple of years to read and begin to digest all that material. However, I doubt it will remove all of your doubts.