We had psychoeducational testing done at the Belin-Blank Center in Iowa. They submitted to our insurance and part of it was paid. Our insurance paid only if a psychologist did the testing (not MS level trained) and only with a diagnosis. They submitted with an anxiety diagnosis, for the sake of getting payment, which was something that was "of concern to watch" per the final report, but not an acute condition.

You might want to call your insurance and see what types of psychological testing they cover, done by who and with what limitations.
HTH