My suggestion would be to experience your own past lives for yourself (possibly with the aid of a past life therapist or counselor). This, of course, “proves” nothing about reincarnation but it can be an interesting experience that at least opens you up to the possibility of more rigorous evidence, such as provided by Ian Stevenson over decades of extremely thorough research. As always, keep an open mind. Religious dogma (of whatever stripe) is the great enemy of knowledge. (So is “scientific” dogma, for that matter. And most scientists are just as opposed to the idea as many Christians.)
Being “regressed” to a past life, by the way, can be like being inside a hologram that you can fast forward or reverse and it’s not like a dream at all. Purely realistic and for that reason convincing, as a lot of various case studies suggest. (Not that this “proves” anything, but it can open your mind to possibilities and introduce you to a new and amazing source of self-knowledge.)
BTW, I seem to recall reading Tom Shroder’s book some time ago and I skimmed through the excerpt posted above. As I indicated, Ian Stevenson is probably the most respected (because most rigorous researcher) in the field. His work spans decades and hundreds of case studies of children remembering (impressively) verified facts from past lives.
(And if anyone’s interested, I’d be happy to share some of mine…)