The only way to simulate accurately on a classical computer is to use global state but this goes against the instruction that the devices must be isolated from each other.

No shit. Of course you can't take a simulation method that takes exponential running time in terms of the size of the thing you're simulating (two Mermin devices), then simulate each half (each Mermin device) independently. If you could split it up like that you'd have a polynomial time simulation method!