We have tried CBT (he's worked with therapists for months at a time) but when he's in the heat of the moment of an anxiety fueled melt-down he CANNOT talk him self out of it. When he's not in this state he could teach a course in CBT. Then he can tell you exactly what he should be doing and feeling to talk himself down.
My DD is exactly like this. Sorry, I kind of skimmed the thread, but it sounds like the psychiatrist does think he has GAD. From my experiences with my own kid, what is probably is happening is that he is anxious at a low level all the time, but in general is able to control it. With the additional stress of the "performance", he loses the ability to use the tools. We did CBT with my DD for 2 years but eventually realized she wasn't able to control it in those high pressure moments (for her it was tests) so the doctor suggested Prozac. It makes a world of difference in her overall anxiety levels and even in the high pressure moments, she is now
mostly able to use the CBT tools.
She is now in HS and gets panic attacks sometimes before a test or presentation. The doctor did say if that continued we might consider giving her a prescription for something like Xanax that she could take on an occasional, as needed basis. But only if the panic attacks were more frequent than once a month, so their threshold is pretty high for prescribing these rescue meds (as it should be).
So I would ask the doctor about an SSRI. I suspect your DS has a lot more anxiety than he is reporting, perhaps even more than he realizes, because to him it is just his normal.