I don’t know about this. You’re suggesting applying reason to an unreasonable situation. You’re not going to “devastate them from the floor” regardless of how solid your arguments are. They don’t acknowledge the existence of logical fallacies and will not recognize being caught in one.
This is an intractable problem and engagement isn’t going to make it go away. I believe the only solution is to promote education and specifically, critical thinking skills. It’s a difficult, long-term solution but I don’t see anything else. Shouting is ineffective, ignoring is dangerous and engaging provides validation.