A parallel situation on a smaller scale.
My RAM 1500 is towing a 4000# GVWR pop-up. Tongue weight <500#. Tow capacity on the RAM is 7700 pounds. Max hitch weight on the RAM is unknown because i'm nowhere near close.
No WDH needed.
But I do have airbags to deal with the (as you know) softly sprung RAM's tendency to wallow and porpoise. It did that with a 2000# (wet) PUP that didn't even have brakes because it was so light. Based on that experience, I installed the bags when I took delivery of the pop-up-ma-hal. The air bags are transformational. I also boost the tire pressure in the rears on the TV by 5 to 10 PSI when hooked and loaded to deal with the weight.
The trailer doesn't tax the TV at all...under any circumstances. I recently towed 90 miles across the plains NE of Denver through cross-winds up to 65 MPH on a road where about 35% of the traffic is semis and other trucks. Zero issues with stability.
So I think your plans to experiment with not using the WDH are reasonable considering that your new TV is such an overmatch for your trailer. But, for the first few trips you might toss the hardware into the truck bed just in case you experience an unexpected case of the wiggles. Also bear in mind that trailer stability has a lot to do with how you load the trailer, whether you're riding level, and what percentage of the trailer's GVWR is dedicated to tongue weight.
Enjoy your new truck. There's nothing like overkill.
P.S. be very aware of those rear fenders sticking out. It's easy to forget they are there, because all the visual cues from the cab can lead you to forget about all that extra width behind you. I see LOTS of duallies with damaged rear fenders from cutting turns too tight.