I forgot about the West Coast - East Coast issues, it had all gone into dis-continuity for me.But we have to remember the mutants as well as the Alpha-Omega bomb, it can be seen as leading up to the original films, even when you consider the ending, didn't Cæser's statue have a tear running down it's cheek? I seem to remember reading that the director had included that to show that the Ape-Man civilisation would not last.
Well on the mutants, in a deleted scene from Battle, I believe it showed those that remained in the city readying to carry the Alpha-Omega bomb and flee to the east coast via underground tunnels. So the mutants in Beneath are the descendants of the human-mutants from Battle.
The Caesar statue was meant to be ambiguous. Either he was crying because humans and apes would now live in peace and equality, or that humans and apes would never be able to get along and in the end we'd get the Planet of the Apes we saw in the first two films.