I would say it's the spring bar tension in the hitch set up. Often performed incorrectly at some dealerships.
From your explanation ,because you are towing with more than enough truck, it sounds to me that you have too much lifting by the bars.
As a quick test, you should try it for a short ride direct to the ball to test it out. See if more hitch weight cures what you are feeling.
While hooked up, too much WD lift will cause your truck tires to easily spin on gravel by increasing the transfer of more weight to the trucks front end. You need to balance your load.
AT 6500# or so, I'll bet the transporter delivered that TT to the dealer using no WD hitch .
What's happening to you now, as the TT travels over imperfect road surface it lifts up on your hitch more so and you feel it pushing you in your seated position, towards the trucks front end. If this is what you are felling, then its an easy quick fix.
Take measurements, start with a level TT. Measure the TT frame to the ground both front and rear. Now,measure the ht. of the inside of the ball mount. At approx. 20" give or take, this will be your hitch height. This is where you start, now move to the truck.
( Load the truck as you normally would to take the wheel well height measurements as well as the ball measurements.)
Use the method in this link, then road test it .
This link is a general setup that will work. You can fine tune at a later time if you find it necessary.
http://davidsrvtips.blogspot.com/2009/02/hitch-setup_2781.html