I have a 2002 Silverado with the 4.8. Earlier this year, I had a leak and had to have a hose replaced and system recharged. Mechanic told me my lines had metal shavings in them and to replace my compressor. It was a dealer, so I went to get a second opinion from an AC expert and he informed me my compressor was running fine and my AC blew colder than his new silverado! Now, when I come to a stop, my AC is blowing warm. I can hear my Compressor Turning on and off. This is what is weird. My power steering is very limited and my voltage gauge is dropping. Once, I start driving again, it will all go back to normal and AC will blow cold. I had my belt and tension pulley replaced thinking it was that. It did not help.
When you stop and the A/C gets warm, then when you start to move again the A/C gets cold. You said the compressor is cycling on and off as it should.
The first thing to look for is to see if the A/C condenser cooling fans are working. If the refrigerant can't cool down when the truck is sitting still then it will give you the warm air condition until you start moving, then when you start moving air is pushed through the condenser it cools the refrigerant and the A/C gets cold again.
The high amperage draw from a bad motor could be the reason the volt meter is showing a low reading.
Have your mechanic check the cooling fan operation.