I was just thinking. For the lo/med/high cooling settings, when you change it from one to the other is it really three distinct positions on the knob, or is it just a continuous range knob with those markings to help you understand it?
If it's continuous, then it really is a thermostat already (although perhaps not the kind you want). If it is continuous and it runs all the time, even on Lo, then perhaps your AC can't keep up with the heat load. What does a thermometer say its getting down to when the AC has been on for a long time?