How you work it depends on the vehicle and the load and the speed. I know nothing about your specific rig or the programming of the engine and transmission computers. I also do not know anything about your engine cooling system. I can only tell you what works for me.
I've a diesel with an auto transmission, too. The engine also has a mechanically driven water pump. I have found that sport mode (what you call tow/haul mode on your truck) works better when towing than the normal mode, which is designed to maximize fuel economy. I suspect you'll find the same. If the terrain is flat, I'll often leave it in normal anyway, but put it in sport/tow/haul for extra engine braking or accelerating power or climbing gentle slopes.
But when the going gets rough, the road gets steep, and the climb gets long, or when the downgrade calls for engine braking to save the wheel brakes, I'll go to manual gear selection and keep those revs up, both for the power and engine braking, but also to make sure the water pump is going full blast to keep engine temps down.
It's lovely having an auto transmission to handle all those decisions. Makes driving so much easier. BUT, and it's a big but, there are times when I want to get all the performance possible, and those computers are just not programmed to provide that.
