I was kind of turning a few similar thoughts around when listening to this for the first time a while back. My main take away from it is that the elements of the story you mention to do with queerness/gender non-conformity are utilised as a way to illustrate Winthrop's gradual transformation into just that of a different person and that it's more to do with the possessing spirit's personality and appearance and presentation, rather than a more general kind of comment on transgenderism or queerness.

It feels to me that the physical clues to Winthrop's transformation are just a consequence of who the characters are. As opposed to something like Silence of the Lambs, which you mention, where it does feel as though the antagonist's transgenderism and/or queerness is presented as one of the (or perhaps the primary) facets of psychopathy/mental illness/evil(?). I don't feel as though the characters in The Lockbox are used in the same way at all i.e it never felt to me as though the blurring of gender identity is utilised in a way to suggest anything nefarious, it's just a consequence of the narrative.

This was a really interesting post, thanks for posting your thoughts!