P.S: In retrospect there's exactly one important canon character in this story whose gender I could freely choose, and I did happen to make her female, but that's not going to be apparent until later.

Clearly, this line is the only important part of this comment. Let the games begin!

(Tonks would be the obvious guess, since there's long been speculation about gender-bending metamorphamagi. But she's presented as female in canon, and Eliezer would probably object to the notion that the mere ability to change body shape would count as changing sex.)