You can reproduce entanglement in a number of local theories. I always mention Einselection in these sorts of threads, because it's a very clean way to get something that looks like many-worlds but isn't hand-wavy and can reproduce entanglement via local mechanisms. In particular, contradictory measurements may take place, but they are forbidden from interacting via superselection rules (such that <x|A|y> = 0 for any observable A for contradictory states x and y). The math isn't as developed as Pilot Wave theory, but it's at least as aesthetically pleasing (deterministic, local, etc.). I guess it gives up definiteness, but in a less objectionable way than many worlds.