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Your answer is essentially what I've been doing. I'll hold out for a bit to see if anyone has a way to make the global setting work before accepting this as answered. Thank you.
See my edit to my original question that sets forth a possible solution. So I guess I've kinda answered my own question. But I'll leave it in an unanswered state for now in case someone has a better approach.
Perhaps it is because my function f[z_] := z^(1/2) is not the principal square root function but instead is giving both square roots. I will edit my original post accordingly.
