How to verify academic history and degree?
What you are trying to do is rather unusual.  In most cases where a degree needs to be verified (admissions, jobs, etc), the person doing the checking has the subject's consent, and normally the subject would just have the university send an official transcript.  In that case the university's "customer" is their own alumnus and they have some interest in being responsive.  In contrast, they have no particular incentive to be responsive to you, and so I'm not too surprised that the process they have is not particularly convenient.

That said, I don't see what you can do except to keep following up with NSC and using their support system.  Or, you could get your lawyer involved, and see if a letter from her can speed things along.

I would note that, while federal privacy laws allow universities to release "directory information" including dates of attendance and degrees, as far as I know, nothing actually requires them to do so.