[johnkosir]

As a retired AC mechanic I think a unit drawing 3-4 amps is not moving much heat I would like to see 10-13 most of these units were designed to run on a 15 amp breaker and you are only allowed too draw  80% so that would be 12 amps. I am guessing you are under charged, A easy way too check would to check the temp of the suction line leaving the evaporator and the temperature of the air leaving the coil  should be  15 to 20 degree difference, another way would be too check the suction pressure, I would use a  pair of pinch off vice grips and pinch off the 1/4" line on the compressor that is pinched with the end welded shut close to the compressor cut the pipe use sulfoss or silver solder to braze on a access fitting with the schrader valve removed cool down the joint with a wet rag being careful not too get any water in side, put the shrader back in, take off my pinch off vice grips squeeze the line to open it up a bit where I pinched it off, check my joint with soapy water  for a leak, put on a set of gauges and check the pressure, my 2004 uses r410 so pressure should be over 120 psi. 1or 2 ounces of freon would make a big difference. If the unit was giving me starting problems I would not think twice about putting a hard start kit on it. 
I have 1 thermostat in the kitchen but I can set each unit too its own temperature and would be surprised if you can't .
 If you change the unit you have too find 1 that will work with that thermostat or fish wires for a new thermostat in the bed room