You assume the relevance of time to souls. Most sources would agree that souls have no form in the three normal spatial dimensions, so it seems inconsistent that they should have any form in the time dimension either. If they've existed forever and reincarnation is correct, then the world population should remain constant. The world population does not remain constant. Therefore, either souls have not existed forever or reincarnation is not correct.
Souls exist external to the normal space-time frame.
Note that I am not necessarily advocating reincarnation, merely proposing a way in which it could occur which would not be subject to the problems you pointed out. I'm willing to grant that it is not the soul that is reincarnated and that whatever it is that persists can move in and out of any living or dead entity in the universe. I really enjoyed your essay on reincarnation, but I have something to add. Without these, I am no more than an inanimate lump of rock. This is where the whole criticism of reincarnation comes in.