Time to get creative and even more proactive.
Contact Army or AF ROTC units at that school or other nearby college? Yes, he’d have to throw himself on their mercy and explain the awkwardness of the Navy unit not supporting him. Advocating for himself is a life skill.
Coaches or athletic instructors at his college?
Has he contacted local high schools with JROTC units to explain his situation and ask for assistance?
Can he come home on a quick trip and do it with his former HS coach or a PE teacher?
Has he presented a written proposal/request to his XO detailing the CFA, the venue, the required equipment, and his plan for social distancing and masking, including all deadlines and the consequences of not submitting a CFA?
It is getting very late in the day to get this done. No CFA, no complete application, no appointment. I am not asking for an answer, at all, but I do admit to wondering why, since he did a CFA the first time around and has known since he refreshed his portal for the next cycle that he would have to do another one, he is now in a difficult situation. Is there any chance - again rhetorical - that in his heart of hearts, he is actually just fine at his NROTC unit, but he felt he had to re-apply through pressure he applied to himself or felt externally, and if he can’t get the CFA done, he’d actually be okay with stepping off the USNA path?
As for the admin, let your son solve that. I think the way it works is he supplies contact info for his CFA administrator to USNA, and they send an email with appropriate links or where to send test results, but someone who is a current applicant or BGO can confirm.