Having moderated a Jeep forum for about 10 years, I've seen my fair share of DW. As was said, all solid axle front suspensions with links can experience it, and most are designed more or less the same. Unfortunately the steering stabilizer only masks another problem. Steering stabilizer's role is to take shocks out of the steering when hitting something off-road. DW is a side to side movement of the axle, and is usually a result of worn bushings or wallowed out bolt holes (which won't be the case with your "new" truck, unless they're defective), or fasteners not torqued to factory spec.
The first place to look is the trackbar, which is what keeps the axle from moving side to side. When diagnosing, I'll typically have someone in the vehicle while I'm underneath row the steering wheel back and forth and I'll look for play, again, starting with the trackbar.
Another thing to try is to rotate your tires and make sure they're the proper air and are balanced. Something out of whack there can trigger DW. I'd also check toe. Although these things don't "cause" DW, they can get it going and once that axle starts moving side to side the only thing that stops it is a drastic change in speed, usually slowing down to around 30mph or so. Ironically, speeding up can also stop it but it's safer to slow down.