Thinking about this deeper, I think the really key element of getting pushed around is rear-steer that's caused by the rear suspension geometry. As the trailer inflicts vertical motion on the tow vehicle, its trackbar has a steering effect on the rear end of the vehicle, sort of a corollary to the roll-steer that we're all familiar with.
I think this is why the OP reported good results towing with his XJ. It does not have a rear trackbar, so it does not get rear-steered by the trailer. I've experienced the same thing with my '98 Durango, towing stable at very high speeds. By contrast, those with rear trackbars have reported unstable towing.
So I guess the rear leaf springs are the key to having a good tow vehicle. I had not previously thought of this because the XJ's front solid axle would make me nervous about towing (i.e., theoretical possibility of death wobble in SFA vehicle). Not many leaf spring vehicles around these days, so the recommendation is still Xterra.