It may be that the neuropsych is not downplaying the LD (since she did give the diagnosis, granted with a low-incidence label), but just viewing the global anxiety as being the more debilitating of his issues at the moment. From your description, that is not an unreasonable position to take at the moment.
He's probably much different at home, because he feels safe there, around his family. You've established that you are trustworthy, and will protect him. New settings can't prove that right away, and if they break trust, it can take a long time to re-build (if ever).
I think LAF makes an excellent point. And yes, CBT, RET, or DBT.