I had a similar problem with my '12, ecsb gas work truck. Has utility body and a lot of weight on the rear axle. Also has 12k winch and bumper up front. Local dealer found a TSB on older (08-10 or something like that ) with weight in the bed. Found it changed the castor enough to cause a problem. They adjusted the castor, and it helped. It's not cured, as when tires are near wore out it creeps back. But overall it's significantly better. Before, if I was going down the highway and it started, I literally had to slow to below 35 or so, so mine was pretty serious. Also significantly worse on wet roads. I think I still have the alignment sheet with what they changed. I'll look tomorrow and post results. This was first noticed around 25k miles on the clock. Trucl doesn't have a dampener, but my 02 didn't either and I never had a problem in 310,000 miles. While I realize my 02 was leaf sprung, the castor plays a big part in how death wobble is achieved.
Do you have anything done to the suspension? Or significant weight added anywhere?