"I make more money than my X does, so pursuing this through the court system would probably do nothing but earn me a monthly child support payment."

In most states, child support obligation is proportional to income (and inversely proportional to parenting time). It could be that the current state of affairs is a fair deal in this light.

I'd look at Jada's questions and make your own assessment of it. Don't fight if there's nothing to be gained.