Man, I totally read the description of the three laws as straight up, "Gender definitely matters. Make sure your game addresses gender, if it's at all interesting to you."
I agree that I'd like more focus on gender, though. What I'd particularly is a playbook or two for someone of the second sex, male for the Old Law, or female for the Law of Eagles or the New Law. I'm hoping the Summer-Crowned fits that.
I think that gender being a Look would not work in this game. In AW, what it means that gender is a Look, is that by default it's about presentation, and by default doesn't matter in the post apocalypse world. In this game, it definitely does matter. It's important for all three of the Laws. Gender is about social role, not look, and about conflicting social roles.
To back-seat game design, what I would do is make it a choice, on each playbook, as part of Rank, right next to choosing your genealogy.