You won't be the first person to experience an incorrect hitch set up from a dealer.
Before you run out buying add-ons. Make sure the WD bars are parallel to the TT frame with a slight bend to them.
I would narrow it down. I would unload the truck and take the rig (TV and TT) for a highway drive. See if handles better unloaded.
If you load the truck back up and take the same ride under the same weather conditions and it rides better, then I would look at the tires.
Check the weight rating stamped on each "P' tire, add them together to get a rear axle rating. Tires are sometimes your limiting factor in your rear axle rating . If that's the case, you need LT tires with a stiffer sidewall and higher weight rating.
If you did individual scale weights, then you know each axle weight of the truck as well as the tongue weight of the TT. Are you overloading the tires ?
If you are using one friction sway, a second might help on a long trailer with bow waves from overtaking semi trucks and buses as well as crosswinds .
If that is your issue now, then a second bar will probably be helpful.
However, if you actually have a true sway issue, a friction bar band-aid might just be masking the problem.
It's also possible, if you are having excessive tongue weight, which causes 'squat'. It makes light steering where the tail wags the dog.