The 5.3 is a good engine and the 6-speed tranny on your 2016 Tahoe will put you in a much better place than the 4-speed in my 2005. We were also towing a slightly heavier TT (just over 7,000 GVWR/5,400 empty). We just had to be patient and put up with 3,500 RPM in the mountains of western North Carolina and east Tennessee. Use tow-haul mode, go down the hills at the same speed you went up, and let the motor do as much of the braking for you as possible. Don't ride the brakes... just stick to the truck lanes and "hang with the big boys and you should be OK.
Happy camping!
Rob