One more thing which may be of interest is that some parents have encountered the same psychologist in private practice and also functioning as the psychologist for their school or district. You may wish to make a list of questions, and possibly have among them, whether this psychologist serves any local schools/districts.

Some families have reported taking a vacation built around visiting a tester... traveling a distance, staying several days, taking in the local sights. This may help broaden your possible selections from the Hoagies list.

Some have shared that university psych departments have offered services at reduced fees. I believe these are typically conducted by students with a Psychologist providing supervision. You may wish to check the website of local universities to see if this is offered in your area.