I think you're barking up the wrong tree. Your AC should run until it reaches the preset temperature as determined by the thermostat knob, then cycle on and off as the temperature rises and falls.
It should not be running that long, freezing you out, then freezing up. Initial run in a hot camper may be a little longer but once cooled down it should not run more than half an hour at a time unless it is severely hot and can't keep up. Since it is freezing you out, it obviously is not severely hot, and has no issues keeping up.
The most obvious cause is your thermostat is not working. However, is it possible that you simply are not familiar with how an old analog AC unit works? As you turn the thermostat knob, the wider the line, the colder the setting.
When I set my AC, I simply turn it to max cold, let it run until the camper gets to the desired temperature, and then turn the knob back until the compressor shuts off. Then it will cycle on and off to maintain that temperature.
