> One possibility, assuming that souls exist, one
> that fits within your boundaries, is that souls
> have very little influence on physical life.
This is an intelligent rationalization. It allows the belief in spirits and reincarnation with an influence on nature just below what current science can measure or discount. It's not very reassuring, however, because it's an adjustable level.
I've heard a similar rationalization applied to God. However, what good is God if he can't be depended on to remain the same today, yesterday, and forever?
What this kind of rationalization does is require God to explain less and less as scientific knowledge increases. Tree gods or fairies used to be used to explain growth of forests, Thor or Zeus to explain lightning and thunder, Pele to explain volcanoes, etc. God or gods were used to explain the formation and characteristics of the Earth, sky, and everything around us. As science progresses, however, these gods or God are needed less and less to explain the universe around us.
In my change from theism to atheism I came to realize that I should follow a different way than the one I had set upon. Instead of assuming Mormonism was true, God existed, Joseph Smith got the Book of Mormon from an Angel, etc. and that reasonable rationalizations should be sought to retain those basic beliefs without denying science, I decided I should ask whether the evidence supported a belief in God, Mormonism, etc. in the first place. I concluded that the evidence for God and Mormonism was insufficient.
I then looked at atheistic arguments against the existence of Jesus Christ and concluded they were reasonable. Not only was Mormonism without valid defense, Christianity was, in my opinion, without support. If millions of people believed so strongly in a falsehood like that I concluded that all religious or pseudoscientific ideas should be suspected of falsehood if they disagreed with known science.
I don't plan to accept any religious idea that hasn't been verified by the best science we have available.
Instead of seeking to find the rare cases where evidence of God, spirits, reincarnation or such things seem to exist (especially if the story is "juiced up" liberally) and ignore the vast majority of unremarkable circumstances or counter-demonstrating examples, you should ask "Is there sufficient evidence to prefer a supernatural over a natural explanation?" With my new perspective, I find in every case I look at the answer is no.