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So, somehow, a subset of reality determines whether or not a choice is A or B while reality as a whole including that subset does not determine whether or not the choice is A or B.

I don't see the logic here. Let S equal the subset of reality that determines choice. Let R be the reality of which S is a part.

S: determines choice
R-S: does not determine choice.
R: can determine choice because it contains S.

Where is the contradiction?

It has to be the agent taking the course of action. The action can't occur due to randomness - if it did, it wouldn't be willed. The action can't occur due to a given set of circumstances - if it did, it wouldn't be free. Therefore it must be simultaneously taken due to a subset of the set of circumstances (the agent and all its internal thoughts, states, etc.) while simultaneously not being taken due to the total set of circumstances.

This is convoluted and I think is in error. Free will requires an Agent that determines the choice and whose actions are not determined by circumstances outside the Agent.
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