If you imagine Im at 0 on the x-axis, and I create an entangled pair, then send one to L and one to -L, then measure both: can't I, at x=0, verify they (don't) match at time L/c rather than 3L/c?

If it were locally probabilistic, then it should accidentally (not) match some of the time between t=L/c and t=3L/c: it cant be both non-deterministic and local if they never match during that time window.

Seperately: fused anyons in electron gases seem to exhibit non-local qunatum numbers. That's why MS wants to use them for quantum computing. Im not sure your sock example is sufficient to explain the stability of topological-regime quantum values against thermal noise and decoherence.