First, may I assume that this air compressor is non-ducted? In other words, the cool air comes out of the roof unit itself and all the controls are on the unit with no wall thermostat?
You mention the temperature drops to 65 degrees and then the fan turns off but the compressor doesn't. Is it possible that the fan is turning off when it's supposed to, but the compressor is NOT turning off? What happens if you turn the temperature dial up after the fan turns off, does the fan turn back on? If the temperature selector has no effect, I would start by replacing the thermostat, otherwise it is probably a bad selector switch.
In any case, it sounds like you have replaced all the logical things, and there is really only one possibility left, and that is the selector switch.