Dear Gordon,
I am now taking the time to read and understand your approach. Fist of all, I have to say that for me Bell's theorem is difficult reading (laziness?). It is why I prefer to refer to Mermin "Hidden variables and two theorems of John Bell (1993)" to grasp the point. May be there is something wrong in Bell after all.
If we accept counterfactual reasoning (do you accept it?), then Mermin's square and Mermin's pentagram tell us a lot about the the structure of observations in quantum mechanics. I went back to the structure of Bell's inequality (in fact CHSH) later, as in Sect. 3 of my essay.
http://www.fqxi.org/community/forum/topic/1789
No need of entanglement here, my two-qubit square has only IX,XI,IZ and ZI as its edges (IX means the tensorial product of I and the Pauli spin matrix along x and so on). If you believe in the virtue of mathematics of giving clear statements (and I think you do), then you should be interested in the graphs, more precisely the maps on the Riemann sphere, underlying CHSH and Mermin. Possibly, this may have impact on your future research.
I intend to give you a very good appreciation taking into account your courage in working on these topics and the enthusiastic style you have. FQXI seems to be a living place where to meet alternative opinions on several important topics dealing with the foundations of physics.
Good luck,
Michel