Dear Edward,
You've written an excellent essay, in my opinion. I agree with your agnosticism about spacetime structure (well, actually, I like to go much further and try to replace the manifold structure with something else at the microscale, but I admit it's speculative). Some of your reflections potentially raise substantial challenges to my own favorite ideas about the role of causality. Of course, I don't mean exactly the same thing by this as you do by "local causality." In any case, I agree that it's less profitable to regard relativity in purely geometric terms than as a way of describing the interaction of actual events. A few more thoughts:
1. I've often thought that perhaps locality ought to be defined in terms of interaction rather than metric structure; i.e., that maybe phenomena like entanglement are indications of nonmanifold structure of spacetime rather than "nonlocality" of interaction in a metric manifold. This view might even be useful to explain things like the homogeneity of the CMB without invoking inflation. However, this is perhaps too simplistic to understand both entanglement and the no-signaling theorem. I think "intrinsic quantum effects" are involved, in a sum-over-histories sort of way.
2. You make an intriguing point with the statement that "it is impossible to say which of the two (or more) measurements is affecting the other. In other words, there is no observable sequence of these spacelike-separated events." Of course, you expand much more on this point later in the essay.
3. Regarding Weinberg's elevation of the property of Lorentz invariance in the S-matrix, I think that covariance in general ought to be reinterpreted in terms of refinements of partial orders, and that the clue to this is the relativity of simultaneity. This doesn't necessarily clash with the lack of an observable sequence, but that's a long story...
4. I agree that Goedel's theorem isn't necessarily links to quantum indeterminism. But I do think it's relevant to physics.
Thanks for the great read! I wish you the best of luck in the voting; I boosted you as much as I could. Take care,
Ben