Part of any attempt to make it work, I think, has to involve moving gender farther down on the list of specifics about a character without completely abandoning it. If you are afraid that if you don't make your characters sexist stereotypes they are going to have no acceptable characteristics that speaks I think to well, sure a gender problem, but also a scenework problem.

Going out onstage to play "a woman" is stupid. Why are you doing that? Why is that the specific you bring into your character? How do you do a scene based off it that isn't just awful? I can guarantee you the woman in your group doesn't start out scenes by thinking "This time, I'm going to play a woman."

Also, starting out a character by thinking about the things you can't do is going to make it hard to actually do the scene.

I'm not convinced that just avoiding having men play women is a bad idea if you really don't have some angle or handle on it, but if you're going to do it I would really focus on bringing some proactive specifics into your scene that provide for the construction of some reason or occasion for the scene to exist.

You're not just playing "a woman" you are playing "this woman." With a heavy dose of the "this." Like maybe start with women who come up in the shows organically because of other characteristics or relationships they have and see how that goes before you try cold initiations with them.

Also if you don't have a coach that's going to make this harder, because one thing the coach could do here is have a candid, private conversation with the one woman in the group (whether that is you or isn't - I suspect it isn't but who knows) to see how she feels about it, because on one hand you probably want to do it with her ideas and feelings in mind but also having the three dudes confronting the woman for permission and validation for how they play drag is just a bad scene.

But yeah, I guess I'd say, start by playing specific women with relationships with people onstage that have already been established. And not just sexual or parenting ones.