I admit I didn't quite understand the objective of the post. Are you inviting to brainstorming??
Here's a quick&dirty one! focused on the conceptual part.
My take on this, is via what's measurable from an inside observer. And if one starts to define the notion of locality, as referring not to spacetime, but to the information space, then a measure of locality can be thought of as a measure of distance between two observers information. As a kind of information divergence.
Then it follows from the choice of abstraction, the any non-local observations simply aren't likely. Because the observation itself, implies projection onto a local observer. (Where local refers to observerID, not to spacetime "points").
Then the remaining problem is that different observer while maintain a sort of local causality, may totally disagree with other observers. And IMO, this disagreement or "inconsistency" manifests itself as physical interactions and "forces" between observers. (And ultimately between subsystems of the universe, since any subsystem can be abstracted to an observer, that observes "the rest of the universe")
The environment (defined as the closest neighbourhood or interacting observers) puts a selective pressure on every observer, to either by internal re-equilibrations come into agreement, or to disintegrate. A kind of self-preservation.
In this way, to have confidence observations of non-local phenonomena, is to estalibsh with high confidence, that an unlikely event has occurred. It somehow contains an internal tension, which I choose to interpret as physical interactions/forces. However inertia probably prevents instant changes. Of course, if an unlikely event is repeatadly observerd! then anyone who is updating his priors will see that the result of this is deformation of the priors. I think it's the same with non-locality and locality.
Edit: Maybe analogous to the idea with gauge invariance that interactions are sort of identified with differences in gauge choices. So from a third observer observing the interactions between many observers, he sees gauge invariance, but still notes that the relative gauges inside the system are related to interactions.
It seems to suggest that there is no gague invariance in the "inside view" (from withing the interaction), but only from an outside view (a weakly coupled observer)??
/Fredrik