I am in the camp of don't settle, because of everything you have written about him over time. He is an abusive bully and won't stop at one thing. He will file again and again. Bullies and abusers don't stop that easily. I don't think its about this thing in particular, he sounds like his life is crumbling and you have historically been his punching bag. You are not there for that anymore and he is placing you back in that role. If you think it is is about the child $$, can you live without it? Would he ever give up his parental rights and let you and the girls move away from him if he no longer had to pay $$?
What is the status on the abuse allegations? Doesn't he have a couple other criminal lawsuits or DSS investigations in the works?