It's not so much the cost of the clutch as it is draining/refilling the system and overhauling the compressor for the clutch etc... Gets very expensive, very quickly... Could be $1K plus!
I would look into the cycle switches first. I would almost guarantee that one of these is your problem.
A way to test the clutch is to run 12V directly to the compressor clutch and see if it gets colder in the cabin when holding it in the energized state. Make sure they have refrigerant gauges hooked up to the low/high pressure lines while doing this so they know if the system pressure gets too high so no accidents happen.
If running power to the compressor directly makes it cold inside the car within pressure specs as seen on the gauges, then it's the pressure switches, wiring, Thermostatic temperature control (if equipped), A/C relay or ECM (if controlled) that is the problem and not the compressor unit.
The Low pressure switch is so that the compressor doesn't run if it's low on refrigerant and cause the compressor to overheat.
The High pressure switch cuts out the compressor should the pressure in the system get too high that it could cause hydro locking in the compressor or cause something to burst/overheat and potentially cause fire or personal injury.
If one of these switches goes, it fails in such a way that the A/C just won't operate until it is repaired sparing you and your vehicle from a possible catastrophe.