As Chevy High Performance states...is it the coolant, or is it the gage, but more importantly, is it the sensor. If the gage is bad, the A/C should not shut off, but if the sensor is bad, the signal from the PCM to the BCM will trigger the BCM to shut down the A/C. In addition, the PCM, controls the coolant gage, and if the sensor is showing hot, the PCM shows hot on the gage.
They can check the coolant temp via a thermometer and verify the sensor via the Tech 2.
Has the dealer checked the fins in the radiator, checked the passages?
If this fails, request the dealer do a complete drain and then perform a vac-and-fill procedure. On some engines (especially inline), there has been problems with large air bubbles causing overheating problems, usually localized to that are of the engine. The vac-and-fill method prevents air bubbles from forming. This condition can come from the plant if during fill the storage tank was switched for the coolant/water mixture.
If this is not the problem, I would say you have a restriction. Airflow is ok through the compartment at speeds, and the mechanical fan does a good job of drawing air, and believe it or not, weighs in less than a electrical fan setup. (Weighed one versus an electrical setup for the infamous H3Lady last year

).
What you describe is not normal. Mine in up to 90 degree weather has remained just below the 1/2 mark.