Plus, it's actually classical: it yields a full explanation of the real, physical, deterministic phenomena underlying apparently quantum ones.

Note that because of Bell's theorem, any classical system is going to have real trouble emulating all of quantum mechanics; entanglement is going to trip it up. I know you said "replicate many aspects of quantum mechanics," but it's probably important to emphasize that this sort of thing is not going to lead to a classical model underlying all of QM.