Hello Brian,
It was a pleasure talking with you on the phone,
I feel sorry for your problem, especially living in Florida, where it is hot and miserable with out your A/C working. You described your problem in great detail, and that made it little easier to diagnose possible solution to your problem. As you said you bought a new switch from a junk yard (U-Pull it) and it made no difference. You described your problem as you would start you car, turn on your A/C and you could hear the compressor coming on, and then you would turn your switch to low or high and it would work it seemed ok, then after a short time, it would shut off and at one time it even blew a puff of white smoke out the vent. That could be form a wire burnt or even a puff of freon. After talking with you for sometime on the phone, it came down to my conclusion is a couple things. I believe either the switch that controls your thermostat/relay is not functioning proper. I would first check in possibly replacing the relay or thermostat switch. I believe it works when cool, and as soon as it gets warmed up, it automatically shuts off. Next and final step, which we cross our fingers that it is not, is the compressor it self is getting hot and shutting off the whole system. A lot of times the compressor can run, but not work properly, and when it gets hot or warn out bushing/barrings etc,,, it will shut down, until it cools. But first step is to check your electrical system, and i believe this is going to be the thermostat or relay that feeds the compressor. You said you have your own owners service manual which is good news, and you can see how it is routed and try and do what you can yourself, but might have to pay that price to have a shop test it with there multimeter and put system under load or pressure, to see why it is shutting down. Sense you had a white puff of smoke come through vent, this could be a electrical short, so you want to be careful to solve this soon, so there is no fire hazard. I hope this helps you some to steer you in the right area to solve this problem. Thanks Mike from fixya