So, my own update:
I planned (to be more accurate, I wrote down ideas for) 3 games about menstruation - two that I'll work on in the future, and a very small icebreaker that I might make this month if I'm on track with everything else. I completely forgot to fix up the story from my last period jam - oops, my bad - so I'll probably make that my first priority.
The icebreaker is called "Menstrual Match", and is super simple: half the group gets items like pads, tampons, chocolate, painkillers, a 'listening ear', and the other half get 'my period', 'awful cramps', cravings, and big moods - they have to go around and say things like "I have my period, do you have any pads?", with the idea being that it will help people get more comfortable with talking about periods. Ideally, you'd play this with a class, before learning about periods - or, I guess you could play it anywhere you'll be discussing periods, tbh. I've got the design and words sorted, now I'm just finding out what I'm gonna do about the art...