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I myself do not see where anything but confusion results from identifying framework choices with hidden variables. If you call a choice of coarse graining of the classical phase space a ‘hidden variable’ you are certainly not using the latter term in the way it is employed in Bohmian mechanics, which was one of Bell’s motivations: the particle positions in BM are NOT part of the Hilbert space; they are an added mathematical structure.
I cannot make any sense of your reference to “which aspect of Bell’s theorem doesn’t go through” somehow associated with “statistical independence of the allowed histories”. Would you care to clarify?
Regarding your views (A) and (B). View (A) I think I understand and probably agree with, but (B) seems confused. There is, to begin with, no “proper” CH framework; have you a particular task in mind? I am not sure what you mean by “real”. Various incompatible frameworks can be assigned probabilities, but they cannot be combined. Regarding “existence” I don’t understand what you are getting at. Given that you have trouble holding (A) and (B) simultaneously, my suggestion would be to get rid of (B), as it doesn’t seem to make sense.
Regarding your final paragraph. I am slightly familiar with boundary conditions on many particle systems in statistical mechanics, but I don’t understand your point. What is your ‘possibility space’? Changing boundary conditions can change bulk properties in an equilibrium ensemble; e.g., when one has a phase transition, but I miss the significance of this for the topic under discussion.
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