I'm going to say you need to consult a lawyer about this.
I do not know if the original child custody court lost jurisdiction once the child went to live with his dad.
However, under the Uniform Child Custody Jurisdiction Enforcement Act, if a child's home state changes, then the Carolina court may have primary jurisdiction to determine child support.
However, that doesn't mean you can't set off any original court ordered child support or back child support.
What you didn't say is whether you ever got a court order for sole custody. It seems if you still have sole custody it doesn't matter if the boy lives with him.
This is a very difficult and imprecise issue because you never got a court order for support which should've been thing-one.
Hence, you need to retain a lawyer. Honestly, it was a bad move not getting a support order and shame on the Washington court for not granting support orders. The court fell flat on this one. Parents cannot waive child support, and, you both owe it to support your child.
At best all you can do is counter-sue for back-child-support and hope that the court will allow you either that or a setoff and recoupment for all back child support against future support orders.
Again no one here can tell you as we're not lawyers in the jurisdiction where he's suing.