Great explanation. I have had several A/C issues with cars in the past. It really helped me understand how the A/C system is supposed to work. On the classic car it was more straight forward to work on. I agree that the techs probably won't be able to help. A/C expert might be the best to consult but because these cars were built for performance, the motor is going to leave some things, like the A/C, in the background if the performance parts are getting hot. Which is actually good because if it cuts the A/C out under heat conditions, chances are you won't burn out your compressor clutch.
I think that may be why Ford built the GT350R without the A/C. They knew the R would be mostly, if not always on the track. No need for another component to overheat and take away from engine performance. I wanted a muscle car and ended up with performance on top of that. I'm learning there are so many quirks to my car that I have to live with because these cars weren't built with daily driving in mind. That being said, I have met a few people that drive their cars daily. Back in the day you could turn the heater on for a bit and cool the car down enough to use the A/C again. Not sure if that would work in this instance but might be something to try. Good luck. I feel for you.