Good day Brobri01,
Here's my experience with a very similar TV and trailer. A couple of years ago we purchased a 2016 GMC 2500HD and an Eagle 338RETS. Very similar configuration as yours. After purchasing our trailer we spent a 10 hour drive pulling it back home. I know your manual, just like mine, says no special hitch is required up to the maximum tow limit. My experience, even with wind and tractor trailers flying by at interstate speeds, was very good. I never felt like I might lose control pulling this trailer. Sway was virtual non-existent. However, I did purchase a WDH for the purpose of reducing porpoising when hitting a dip or bump in the road. It makes a pretty big difference with that rocking that sometimes happens. One thing that did scare the snot out of me was, even after installing the WDH, was going on a long trip with brand new tires with deep lugs. I would never do that again. After a couple of weeks of travelling and few thousand miles, the rubber stiffened and the sway disappeared.