Hm. I find it interesting that you say the scientific part of you is the part which has trouble with reincarnation. Imo, science can explain reincarnation. The first law of thermodynamics states that energy can not be created nor destroyed. Everything we are is energy. Upon death, our physical energies (matter) reincarnates as it decays and gives rise to new life. Our "etheral" energies (consciousness and spirit (spirit is a bit more abstract and not easily grasped in empiricism so we'll leave it out for now) are given back to the pool of energies which give rise to consciousness in the first place. We are beginning to understand consciousness as something of a quantum field which gives rise to existence - but its yin/yang in the fact that existence also gives rise to consciousness. This would be where we return to and eventually depart from as we are given new life. Imo, its the Spirit, or the spark that gives life to all which goes on for reincarnation and the consciousness dissolves into a "memory bank", something like the new age Akashic Records.
What interests me is that I believe time to be cyclical, all things repeating - perhaps slightly different each time, but repeating nonetheless. That said - one individual would eventually experience the life of all all points of consciousness throughout the universe. So, things like past life recall are interesting to me... what's to say that we've not all already been one another?
I feel like I made no sense XD
RE: Reincarnation as mentioned in the Bible and Bhagavad - Gita