I am wondering if every contextual theory that reproduces QM is NON-local and reciprocally. Otherwise, when is contextuality equivalent to non-locality? And moreover, how much nonlocality is encoded into contextuality? Are every non-local quantum-like theory contextual?
I believe the answers to your question can be found in Locality and realism in contextual theories by Dick Hoekzema. If I understand it correctly, the paper does show that contextual theories must be non local.