What hechosedrugs said! When you said he wanted to pay the mortgage and not child support, I immediately thought "He's doing that because they can garnish wages for child support, NOT for a mortgage."
He may spend a $1M on a lawyer, but no lawyer will be able to take away the fact that he was fired from his job. And I'm sure there was a long documented process about that too. Does he honestly want to drag this out in court and open the possibility that his drug use becomes public record? Look what happened to Jack Ryan, the politician.
I'm not a lawyer, but it appears that you are in a better position for negotiation than he is. Don't let his delusions become your truth.