Fascinating article. Your definition of gender, especially, blew me away. I've never thought of it quite that way before, but it's brilliant.
The above highlighted section complicates the issue though, no? Trans women who "pass" would be identified as female by a lay-person's reading of sex. And would face most of the issues you describe precisely because, at a glance, they'd be read as women.
I agree with the fundamental argument, trans women are not identical to women, and there are areas in which those differences are important and negatively impact women when ignored (sport and healthcare are good examples).
But trans women aren't identical to men either. And failing to recognise that does create situations that would put them in danger. Don't you think we need an answer that's more nuanced than "they're male, so should be treated as all other males in all situations"?