Of course besides the above, my hypothesis can handle some sort of "uplift" without new spirits being born or perhaps some other ideas as well.
Taking the scripture literally, will Neanderthals and all the other species that have existed and died out rise in the resurrection?
I'm not aware of any scripture that addresses the problem. There could be resurrection for preAdamites and preAdamite species, there might not be. Wouldn't matter either way imho and neither would advance or detract from my hypothesis.
Doctrine on D&C 77:6 (D&C Institute Manual) refers to that time period in a sense that nothing we worry about today or during the various dispensations applies; it's a time when the earth is being prepared for the the habitation of men.
Doesn't the LDS Church still claim there was no death before the fall of Adam?
Yes. I claim the same in my hypothesis.
Yet the evidence that things have lived and died for nearly a billion years seems overwhelming. How do you reconcile that?
Everything happens exactly as science says it did. Same for LDS doctrine. PreAdamite homo sapiens are part of the creative period.
The creative period in which there is death and evolution comes before Adam. Recall that 2 Nephi 2:22 posits a state before creation was finished (the creative period) and does not apply the property of no death to that state. The property of no death is only applied to the finished state of creation in that verse. Then you have Adam and the state of no death. And then the Fall after which death and evolution proceeds apace.
What comes directly before the Fall? The Garden state of no death. So, as long as there is a state of no death directly before the Fall, then one's hypothesis of creation is well on the way to being in harmony with LDS doctrine.
The Abraham 4-5 version of creation is also friendly to evolution. The Gods waited until the elements obeyed.
I think the big unanswered question is whether or not the Garden was just a small locality or was it the whole earth? The doctrine seems to support both. For example, what were Adam and Eve cast out into? That would imply a local Garden. That is traditionally the avenue I take. However, each possibility solves a problem and creates another one. There are plausible answers for each.