Hi Steve,
I read your excellent essay weeks ago, and have been meaning to write some comments... So here goes:
First off, I'm quite heartened to see you further develop this analogy you're building between Bell-inequality violations and the cosmological question of why causally-disconnected regions of the universe look so similar. I recall an off-hand mention of this point in one of your previous essays, but here you've really laid it out quite nicely.
Other points of contact with my thinking are your focus on violating "statistical independence" (as you know), and the idea that some gauge symmetries may be a mere "modding out" over important hidden variables (as you may not know). Have you considered U(1) in this context, and whether or not one might expect QM to fail at timescales approaching the inverse Compton frequency?
Next, some quibbles:
You set up your main point in terms of nonlocal correlations in physical systems, but in all your examples (and even in the first paragraph of section 2), you really always come back to nonlocal correlations in the *initial boundary conditions* of a system. After all, in order to carefully talk about separate systems being "independent", you're really using counterfactuals, in which case it's crucial to specify what's "given" in the problem. And what's given in your examples, is, apparently, no information before the initial boundary in question. After that boundary, you point out that correlations can evolve dynamically, which makes discussions of "independence" much trickier.
Sure, you then point out that you want your nonlocal correlations to be "conserved" by the dynamics, but in the case of the Big Bang, at least, that seems to be too stringent. Wouldn't you be happy with nonlocal correlations in the initial boundary conditions of the universe that no longer held true after the universe started evolving?
But that just raises the question of why you want the dynamics to automatically "maintain" such non-local correlations in the first place. After all, the correlations you propose seem more 'powerful' than mere dynamics. Why couldn't you start out by applying those correlations at all times, then use the dynamics to run all those correlations backwards to the initial state, and derive *new* non-local constraints that apply at the beginning as well? (Crucially, those new constraints will depend on the future dynamics.) Of course, this leads you right back to the retrocausal stories you're trying to get away from, but it gives you a lot more wiggle room where the dynamics is concerned. (Maybe you could even give up dynamics entirely, as I'm arguing these days... :-)
Finally, I have to say that from my viewpoint, you never adequately addressed the conspiratorial aspect that would be required for your version of Bell-inequality violations to work -- simply because the physical mechanism that sets a1/a2 need look nothing like the object being measured in the apparatus. (It need not even be the same type of particle.) There are *so* many ways to trigger the a1/a2 switch that forcing a correlation between lambda and every-possible-trigger seems conspiratorial indeed. (At least, without retrocausation.)
Maybe PBR would be a better test-bed for these ideas. After all, statistical independence is even more front-and-center in that experiment. That said, I have a gut feeling that PBR carries the seeds for a "no-go" result for a non-retrocausal violation of statistical independence. The non-local correlations you'd need for one PBR measurement might be provably different from the correlations you'd need for an alternate PBR measurement (say, where some of the signs were changed in the construction of the measured basis). Still, this would be a very interesting result, either way.
Hope we cross paths again soon! All the best,
Ken