J.W.
You have the same options as everyone else. You either go to the in network providers or you pay the out of network price. Your son's circumstances have no bearing on the outcome.
Without taking the time to find your other post I have to wonder if you are not being too specific in your needs. My kids have all sorts of issues the worst being Autism spectrum. No one has ever recommended a developmental pediatrician.
Okay that other post wasn't helpful and really long.
Start with a neurologist to rule out issues of the structure of the brain and then most on to a psychiatrist to go with mental. You will find there are a lot more of them that are covered than some obscure title as a developmental pediatrician.