Hi Joy and Tom,
On thinking like Einstein, it is worth updating the EPR argument from quantum mechanics to quantum field theory (I've re-attached a copy of the original EPR paper for convenience so you can see that it is a QM based argument). Dirac's equation of 1928 raised a warning flag about the effect of relativity on QM before the EPR paper, and the first quantum field theory (QED) was in place by the time of Bell's 1964 paper (the Nobel prize for QED was 1965). But despite this, Bell's choice of manifold S0={-1,+1} is effectively based on the assumption of a non-relativistic classical physics analogue of non-relativistic QM. BUT this is wrong because the required classical physics analogue should be of relativistic quantum field theory.
In QFT - and this applies even in the deceptively non-relativistic case of stationary electrons - the electrons interact by virtual photons that can become virtual electron-positron pairs. In this QFT expansion, positrons can annihilate the original electrons, turning their electron partners in the created pair into the new correlated electrons. In this process, the spins of the real electrons - i.e. not the virtual ones - are constrained to be in the same S=0 singlet state. If each spin was also constrained to remain in the same direction THEN the manifold would be S0, BUT each spin is actually free to lie on any point of S2 within S3. Any physically correct classical physics analogue - i.e. what Einstein was after - MUST reproduce this, which Bell's does NOT, but Joy's does - ergo, the former is wrong and the latter is correct.
But in addition to the S=0 condition, the QFT dynamics is also constrained for there to be 2 real electrons - it is easy to forget this, but in QFT a virtual photon can produce a particle/anti-particle pair for any of the charged fermion types. These virtual pairs must annihilate to leave 2 real electrons, and this QFT constraint MUST also be reproduced in the hidden variable classical physics analogue of the QFT dynamics. In analogy to the correlated spins effectively exploring the global structure of S3 through the classical physics analogue of the QFT dynamics, the changes in particle type also effectively explore the global structure of the "particle space". The constraint of S3 or S7 should similarly apply, implying that the internal particle symmetry space MUST be S7.
The scenario given in my essay (and paper) is of the correct form for a classical physics analogue for QFT of the EPR scenario, but it is also the predicted scenario of a pure geometric 11D GR without additional fields.
Best,
MichaelAttachment #1: EPR.pdf