Mechanical issues aside, one word: Oscillation !
Locally on a certain section of road my previous Chevy 1 ton (leaf springs/unloaded) would go into a crazy oscillation involving both ends, I tried braking and slowing down, speeding up to break the cycle and the only thing that worked was to slow WAY down.
These big heavy trucks have a " not so sweet spot" on certain road surfaces that make them act possessed !
I thought those days were over when I bought a Ram 2500 with coil springs. Not so fast... I still get oscillation on this section of road but it`s considerably less with this truck, especially after a installed the softer Thuren/King shocks 3in. system!
Here in the mtns we often carry about 250lbs of sand bags in the bed for snow/ice traction with a side benefit of smoothing out oscillation on these bad sections of road...
After ruling out mechanical issues try the sandbag trick (they`re cheap at Home Depot, Lowes, etc) and let us know how it works...
Also, I agree with Mc Broom, too much air pressure when empty is also a big contributor to the problem as well....