I have encountered this before. Twice actually. Once was a psychologist in NJ who I was able to get into a closed network (BCBS) because he specialized in EMDR.. another was a psychiatrist out here in upstate NY where we have shortage of psychiatrists.
Sometimes you can get a provider into a closed network for a couple of different reasons.. one might be lack of that same provider type within a certain area. Carriers usually have their own criteria for example, out here we have ONE dermatologist within 150 mile radius. Another reason might be a type of service that provider does that other providers of same type do not do as was my case with EMDR. There does have to be a good reason for them to credential into a closed panel. You actually would do an appeal the same way you would do one with a claim. You assess the services and the area, determine if there is a special need for that provider or a special service they provide that is not common in the area, and then you appeal to the carrier with your documentation/research.