Edwin,
In regards to Bell, let me give you something to think about, in the realm of truly macroscopic objects like idealized coins, rather than electron spins.
The correlation given for classical entities is a triangular function. The correlation given for quantum entities is a sinusoid. A triangular function has a Fourier spectrum, consisting of odd harmonics of the sinusoidal fundamental. Consequently, even a crude lowpass filter (smoothing operation) applied to the triangular function, will convert it into a sinusoid. Thus, the only difference between the triangular and sinusoidal correlation functions, is a lowpass filter.
Now Shannon's Capacity theorem, reduces to the uncertainty principle, when only a single bit of information is recoverable from a message. Any such message is inherently band limited (lowpass filtered). But was the filter applied at the transmitter or the receiver? If it was applied at the transmitter, then the "single bit" is an intrinsic property of the entity being received, not the apparatus being used to receive it.
Now consider making a very noisy, time-bandwidth limited measurement (limited at the transmitter, to contain only a single recoverable bit of information), and then trying to "decide" whether the measurement is +1 or -1. As noted above, a simple lowpass filter will convert a triangular function into a sinusoidal one. But does one apply the filter to the measurements or the discrete decisions derived from the measurements? And how, exactly, did one make the decisions? More importantly, in this limiting case of only a single bit being present, can one even separate the measurement and the decision making processes, and thus which data set, the measurements or the decisions, are to be filtered? If filtered decisions are used as input to the correlation computation, the result will be sinusoidal, though perhaps not "normalized".
My point is that, the correlation may result from the peculiar nature of attempting to "decide" the difference between a measurement and a decision/index based on the measurement, when only a single bit of information exists, rather than from any considerations of the physics per se, which is merely the carrier of the one-bit message.
Rob McEachern