A lower gear may make the shifting less and better per say. A 6 sp will be better than the older 4 sp frankly. BUT, as noted, with 3.73 gears, the DOD/6th will be useless unless you can get or have 4.33 or 4.56 gears. Otherwise it is too tall, you will not have enough rpm to make the HP needed to move the load.
I move 6-8K with my 2000 C2500, a vortec 5.7, 255/330 hp torque spec, 4.10's and a 4 sp auto. I am usually no slower than 50 on the steeper 3-4% freeway grades, in 2nd, doing 4-4.5K rpm. I can go faster, but for what I have drivetrain wise, not sure the extra strain is worth it.
I drove similarly with my 05 dmax, and 96 6.5td, and my IDI 7.3 in my navistart dumptruck. I find a gear, rpm that pulls the hill at a given speed, but not losig speed, overheating etc.
I personally would pull said TT with a 6.0 sp 4.10 setup
Marty