I am the original owner of a 2015 LT with trailer package and auto level control. My vehicle now has 90k miles and has never done the described test sequence each time it is started. The system has always worked correctly by pumping up
the shocks to level the rear when weighed down by a trailer etc. It does take quite a bit of time to bleed back down after the load is removed unless it is being driven.
I should mention that I replaced the super stiff rear trailer option springs with #5321 Beltech springs to lower the rear 2" and greatly improve the ride. To recalibrate the height adjustment rods I purchased a couple of 3" long 1/8" all threaded bolts from Home Depot, cut the heads off and transferred the caps from the oem rods. I think the adjustment was about 2 .75" from socket to socket center