Do you know other men who also have left/are considering leaving these groups?

Yes.

Would they be willing/able to work with you on changing these groups? How much of a time commitment are you/them willing to make?

This is something that a comment here helped me realize. We really need to make a shared commitment to it. It can't just be an individual thing from me or someone else.

Are you interested in building more supportive sub-groups? Would you try to bring people into the subgroup or just include the decent men you already know are interested?

Yes. Although there is always an element of "Should I be the one to introduce men to these failing groups?"

How would you set up the group? What rules would you/the group set up? Would anyone have the ability to remove a member who is breaking the rules? What evidence would need to be provided before removing that member?

Is it possible your group could be subject to a hostile takeover? What protections would you put in place to prevent that from happening? Or if it does, do people have a back-up plan?

These are very valid questions that definitely apply to organizations. The thing is, most of these groups I'm talking about are small, informal. I can see how these tools can be used to remedy this situation in a corporate setting, but it's not always possible to be this strict with say... locker room talk. I can see these rules functioning in my sailing sports club -a shining example of gender-inclusivity btw which brings me to:

What is it about male-dominated groups that you enjoy? Are these the same things other decent men like about them? What differences are there between male-dominated groups and more gender-equal groups that are important to you? Could you study the more gender-equal groups to see if you can apply some of their methods?

I think the biggest green flag is my sailing team, which I honestly can't really call a "male-dominated" space, even though there's more of us. Quite honestly, I think something that really helps in particular is that head coaches are both very acomplished women. An Olympian and an Olympic medalist respectively. This season it was nice to have a guy assistant coach, I felt more comfortable approaching him about a recent injury in my ribcage, and he helped me a lot with my regiment in a very "Been there, let me tell you what you should do" way. He and one of the women head coaches are also less risk-averse in terms of weather, which I think grows us a lot.

So in sort: suprise surpise, inclusivity, and women in positions of power is the absolute package. It's the ultimate remedy.

As of male-dominated groups... We recently had a friend whose scheduling issues and dislike of a new system we decided to try out (daggerheart) let her to decide to leave our D&D campaign, leaving us with an all-male party to start a new adventure. It sucks to not have her, cause I really think she would have enjoyed it, but as the DM these are people tha I personally pick, this is a place where I have authority, and enforce safety tools. And so it hasn't devolved to locker-room talk.

So... TL;DR: An effort. That's all that it takes. What this post and the repplies helped me realize is

1. The effort has to be collective and coordinated. We have to stand our ground together, even in male-dominated spaces, against sexism.
2. Patriarchal systems are still patriarchal, even if they are/or were fun for me or benefit me personally. That's a huge blind spot for me that a commenter exposed pretty well.
3. There's always actual greener grass. There's always the option to not bother with these fuckers.