I just thought of something else. Could the brakes on the trailer possibly be stuck partially on? I know me and my father pulled a smaller u haul trailer with his 05 2500hd and the brakes were stuck partially on (surge brakes). The truck was working 10 times as hard as it should have been. We found the brake issue after we finished the almost 150mile drive when the rims were starting to lose their paint from the heat.
I think that there would have been some indication if that was happening. Like you mentioned, hot paint, burning smell, etc.