The 5.3 Is an OLD outdated motor, that makes pretty horrible power either way, that putting 7k behind it in the hills will make you want to bite your nails off.
The op has a 2016 ET3 5.3 engine not a '2003 5.3 with a 6/8 speed tranny. Nite and day different.
I see your posting this on other 5.3 threads so enlighten yourself on the new gen EcoTec 5.3 subject. The new ET3 5.3 puts out 355 hp and 383 pound torque.
My wife has a 2016 1500 just like the OP only its a 4wd/6 speed tranny. It comes with a 9400 lb tow rating also. The ET3 5.3 handles that weight fine in the hills. I had to add Sumo springs to the 4000 RAWR with a 3460 lb axle load. Most 1500 4x4 trucks sit level when empty and can sag with 1000 lbs in the bed.
The OP won't have any problems towing a 6192 lb dry weight plus say 1500 more for loading = 7692 lb wet weight trailer.
The ET3 5.3 is a strong towing engine for what it is so forget about using OD when towing.
I use manual mode with the 6 speed tranny and 3rd and 4th towing the 10k hauler with my blue tractor in the hills and 5th out on the flats. Eliminates all the up and down gear shifting and TC clutch lock and unlocking events.
