Pood said:
"The only form of necessity I recognize is logical necessity ..."
Okay, then you surely realize that there is no sort of necessity (logical, entailment, or otherwise) in your earlier statement: "if you replayed a series of events, with the exact same antecedents, then some person P would always choose X." A closer to necessity form of that statement would be "if you replayed a series of events, with the exact same antecedents, then some person P would always do X." It is closer to necessity in the sense that it is more trans-perspectival. The revised statement is more trans-perspectival in that it is a statement which is coherent both from the modal determinism and the nomological determinism viewpoints. The revised statement also avoids begging the question with regards to those who regard the act of choosing as presuming an actual indeterminateness which provides for actual (and, typically, actualizable) alternatives.
But, then, there is this earlier statement: "The compatibilist is simply pointing out, however, that there there is no
necessity in this choice — the choice x was, is, and always will be,
contingent — which automatically means it could have been otherwise."
First of all, given that the modal approach is not logically necessary, the cited statement is more accurately expressed as "... there is no modal necessity in this choice". Secondly, the remark "contingent ... automatically means it could have been otherwise" is also not logically necessary. From the nomological determinism perspective, even granting the contingency, it is false that "it could have been otherwise" insofar as "otherwise" at least implies there having been the very sort of indeterminateness which is denied under nomological determinism.
For that matter, and certainly from the perspective of the nomological determinists, there is nothing about the modal perspective which necessarily entails that "it could have been otherwise" within the context of this universe.