Every day I wake up, I hate Jason even more.
Do the right thing: read the room, resign and let a woman take the role.
Given he wants to talk about the menopause, I'd argue that it shouldn't just be a woman in the role, but an older one. I mean, as a woman, I know how awful periods can be (especially as a teen, so many memories!) and I have an idea of what the menopause will be like, but I don't have the lived experience (yet).
This is a role with a stupid sounding title that can only be made to sound less stupid by appointing an older woman who brings gravitas from her life experience.
A woman with medical experience would be ideal, or one with experience working with girls (e.g. former teacher). Screw this project management malarkey: few very women get to menopausal age without knowing how to organise the hell out of it anything. You don't need a relevant degree (who wrote this damn job spec?) to understand what women's issues are like and be able to organise distribution of sanitary protection to those who need it.
And people who menstruate takes the focus away from teenage girls, who let's face it, are the ones mainly suffering from period indignity. I don't mind saying "girls, women and any other people who menstruate" to include transmen and non-binary people, but you have to lead with the people who are most heavily affected. Girls and women. Being inclusive doesn't involve excluding the majority.
It's worth noting that whilst transmen can experience periods, some take high enough levels of testosterone to prevent them. So periods really do remain primarily a female issue.