I just pulled southern Colorado last week with my 2500HD with 6.0 liter gas engine. I'm pulling considerably lighter than you but I did learn a few things.
Going out I just left it in tow / haul and tapped the brakes to downshift and as mentioned above, if speed picked up too much, I'd step on the brakes pretty hard and get below my comfort speed and start all over.
Coming back, I put my transmission in manual shift and used the toggle to shift up and down and it worked a lot better. It was easier to control speed down and my trans temp was 20 - 30 degrees cooler going up compared to using the automatic setting.
I got up to ~4800 rpm going both up and down. It sounded too high but I figured they make 'em to do it.
I kept my foot in it when needed.....