Peter Morgan 19 January 2024

Tim's approach seems to me a usefully dynamical complement to 't Hooft's more Computational Automata approach, but IMO it would help if he were to consider the use of the Poisson bracket as a way to introduce noncommutativity into classical mechanics, as I do in my Annals of Physics 2020, "An algebraic approach to Koopman classical mechanics", arXiv:1901.00526 (DOI there).
Also IMO, his description of the violation of Bell inequalities would also benefit from considering the argument in my JPhysA 2006, "Bell inequalities for random fields" arXiv:cond-mat/0403692 (again, DOI there), where I point out that in what he describes above as "the measurement settings can be varied independently of the hidden variables", 'the measurement settings' includes both the obviously visible and recorded choices by Alice and Bob, commonly just '0' or '1', but also the unrecorded internal degrees of freedom of the measurement devices, which might include fractal or near-fractal structure. It's enough for the violation of the Bell inequalities if the central apparatus 'conditions' those unrecorded degrees of freedom of the measurement devices.
It seems to me not unreasonable or even reasonable to claim that there is a fractal structure, but we can acquire only coarse-grained statistical information about that structure, so that we are all but compelled to use a stochastic process approach. I won't belabor that here, but I have given recent talks in relatively low-key seminars that outline some of these auxiliary ideas.