Volunteering won't do it. The defiant nature of the leaders here will just give you more work, laugh at you struggle, and will try to make you quit.
You have to put yourself on the chopping block by simply reporting your manager to Employee Relations. They will take the side of your supervisor, BUT you are a target now. A person who doesn't go with the flow, and can potentially expose them. Therefore, becoming a financiql liability and a source to empower others.
I guarantee you will be on the next list.