I have a trailer in that range. I towed it with QCLB Titan for one season, and got thrown all over the place. I tried my dad’s Super Cab F150, and got thrown all over the place. I tried it with a neighbors QC Sierra, and got thrown all over the place.
Any amount of side wind moved the whole rig. Any large rig passing sucked me in or moved me over.
Behind a 2500 all that went away.
Instead of a new truck you could have just bought a proper sized spring bar WDH with built in sway control and set it up with TV & TT WD. Set according to scale results replacing unloaded steer weight, getting drive below rating, and getting TW in the 10 to 15 percent range would have also made all that go away on any of those three trucks.
Not hating just saying. Its the physics of it. People often talk about a payload sticker to. There is value in that for warranty & such but keeping the main thing the main thing its steer, drive, & TW percentage as measured by change in axle weights from unloaded truck to loaded truck. Then divide that number into the gross trailer weight for the TW percentage.
Thats the proper accurate way to do it because a WDH makes TW dynamic not static. To be fair while all the 33' floorplans I've towed were solid when I did an odd 34 and an odd 35' floorplan they were a lil too much for the truck. Ok for a short level non windy transport but nothing more. Also that said I agree with your first reply in this thread; "32-34’ trailer is a big trailer for a half ton to handle no matter the weight. All that side surface area is hard to control." So maybe I'm splitting hairs here but I've always been successful with the 33 FPs and I mostly just want people to have the right focus on setting up their rig. Last just because you are not feeling it the HD doesn't mean its not there. It still is just to a lesser degree due to the heavier truck and stiffer suspension. Setting it up via scale results would still make it a safer more stable rig. You might not immediately feel it until you have to do an emergency swerve around etc but its there. And well its your family. Best
Edit: On a side note for readers as related here. I sometimes set my hitch and load to be a little over GVWR even though I could set it up to be below GVWR. Getting to a better axle weight bias more on the steers and truck in general. The reason is I'm more concerned with the most safe & stable tow and making sure the tail can't wag the dog. Being a little over on the GVWR doesn't bother me. I'm more common sense, what works practically, spirit of the law minded than letter of the law legalistically minded. Certainly they both have their place. FWIW I have even been through scale houses over GVWR as all they were concerned with was axle weights to axle limits. At least with respects to single pull pick up and campers.