You have no leverage. Your bluff was called. Your threats weren't backed up. You chose your hill and died on it, so to speak. It may be harsh of me to say but

You have no leverage. Your bluff was called. Your threats weren't backed up. You chose your hill and died on it, so to speak. It may be harsh of me to say but IMO you should leave ASAP. Walk. Line up some work for your people, if they are with you still. You lost and it is unlikely your situation will improve at the leadership level. Also, stop framing it as them being right/wrong vs. you being sane/crazy. That is a false dichotomy and largely irrelevant to the mechanics at play.