My wifes 2016 1500 chevy 5.3 has 355hp and 383 torque (same as the OPs truck) with a 6 speed tranny and 3.42 gears.
It pulls a 10k car hauler with my 11' 6 ' tall blue cab'd tractor with around 8500 lb on the trailers axles and 1080 on the trucks 4000 rawr. The longest runs I make is around 250 miles out. Nothing wrong with the 3.42 gears with the 6 speed or the 8 speed tranny. IMO some are still stuck in the 3.42 gears and the old 4 speed tranny era.
I doubt you will like pulling a TT with a 7150 dry weight that may weigh in the 8k-8.5k range after loading for very long. Its going to struggle in the hills and in high head winds.
GM max tow (NHT) package comes with higher 7600 GVWR and 4300 rawr. The 5.3 with 355/383 numbers does a good job for what it is. The optional 6.2 gives us a 420hp/460 torque. The 6.2 with the NHT package 8 speed tranny would have no problems with that size trailer.