I also live in the South and I have a 2003 Avalanche and a 2004 EXT.
The one thing I have done to both of my trucks that has helped with both the a/c performance as well as low speed and idle engine temperatures is to replace the old, worn out OEM standard duty engine fan clutch.
I found long ago that the OEM standard duty fan clutches were designed mainly to be QUIET and they do not pull as much air through the a/c condenser and engine coolant radiator as a SEVERE DUTY fan clutch.
Add to that the fact that your existing fan clutch, if it is the original one, is very likely worn out and it pulls even less air than a brand new OEM standard duty fan clutch.
When I first bought each of these trucks used, both of them suffered from poor a/c performance, especially at idle and during low speed operations.
They both also suffered from the engine coolant temperature rising in stop and go traffic in the heat of summer or during extending idling.
Installing new, direct replacement OEM standard duty fan clutches only helped to a small degree.
Now, both trucks have a
Hayden Automotive 2786 Premium Fan Clutch installed.
The a/c is now cold at extended idle and during low speed operations and the engine coolant remains rock solid at all times.
Now understand, the SEVERE DUTY fan clutch will produce more noise than the OEM fan clutch, but that is because it is pulling a lot more air through the system.
I find the severe duty fan clutch to make more noise at first cold start up until the engine reaches normal operating temperature.
Then the fan gets much quieter.
Until, the engine is placed in a high heat load situation like extended low speed operation or idling during the high heat of summer.
At that point, you are certainly going to hear the engine cooling fan roar quite a bit more.
But, that sound you hear is the severe duty fan clutch doing it's job.
Pulling a lot more air.
I am totally OK with that as I sit in stalled traffic up on the highway for an extended period of time and my engine stays cool and my a/c stays cold.
I have to wonder if all of the other drivers with me in that traffic jam can say the same.
And by the way, a conversion from a fan clutch to an electric fan system is also a viable option, but you will need to understand everything you will need to buy and do before taking on that project.
Or, you can just spend the $50 for the severe duty fan clutch and see if that solves your problem.