"I've certainly encountered TERFs who believe that brains are wired in radically different ways based on sex."

Can you cite one who has publicly shared that view? I was under the impression that TERFs are above all anti-essentialist, like you. How can anyone believe that trans identities are not physiologically/genetically based? Where else does the knowledge of misassignment come from?

I believe that either (i) trans people really do feel something essential, or (ii) they only think they do but there's no there there. You are saying that they really do feel something, but there is nothing there to feel. That does not compute.

I will leave the issue of nature/nurture; I believe it is irrelevant to the question of hard-wiring. In some ways, culture counters our hard-wiring, and in others it channels or support it. Circumstances vary, and we are a uniquely adaptable species.