My 2010 4.8 had same issue recently. The clutch went bad, instead of replacing only the clutch I replaced the compressor (complete with clutch),
receiver drier, o-rings. PITA!! Weighed in the correct amount of refrigerant and about 2.5 pag compressor oil. I could only get 56 degrees on either side of the car which really made me crazy. The compressor also came with a new txv which requires removing the dash, no way that was happening.
Long story short, the additional problem was the heater control valve, easy to change and holy crap!!! 36 degree air.



Check the temp on the driver and passenger side separately, if there is as much as a 5 degree difference you probably have a bad heater control valve.
I"m a commercial HVAC engineer by trade by the way. This wasn't as fun as I thought. I actually purchased the compressor kit from amazon of all places and couldn't be happier!! $284.95 Not Bad...


Also I didn't do any programing at all.