Well, I think a baby that dies just dies. The end. Very sad, but just the way it is. But let's go with my boyfriend's worldview for a minute, since he believes in reincarnation, and we've discussed it a number of times.
According to him, a baby that dies (or anything that dies) releases its spirit and re-joins the collective spiritual consciousness of the world. Some time later (as "time," the way we understand it, has no meaning in the spirit world), the spirit comes into something else that is being born. It could be another human baby, an animal, a plant, or whatever. It could happen instantaneously (again, from our human perspective of time), or it could happen thousands of years later. Spirits do not have "lives" and singular consciousness during that period, they are just part of a collective whole.
While there are still some obvious logical problems with this framework, it makes a hell of a lot more sense than spirit primary schools and backwards aging and whatever else you're proposing. I find your view needlessly complicated, and I almost wonder if you are joking.
ETA - At any rate, I'm glad you're feeling okay mentally now, and that you're so willing to talk about your experiences. That is valuable.