An excellent and thought-provoking essay, thank you very much. Yodu're right that the society would greatly benefit from promoting (and paying for the education of) polymaths.
I am intersexed, so if the only factor in gender was socialization, I would be fine as a man. But I knew that I was different, and not just because I possessed a well-hidden pair of uteruses. There are many men with that syndrome (from diethylstilbestrol poisoning) who never question their gender.
And there is the famous (Dutch?) study of 40 or so MtF transgender corpses, showing the female-typical neuron count in (if I recall correctly) the basal stria terminalis.
A polymath trained in psychoneuroendocrinology, and statistics, and gender studies, and psychology, with access to a functional positron emission tomograph, might know what to do with this.
Thank you!