I towed at 37' Heartland Cyclone toy hauler with both a 2004 and a 2014 Duramax and I cannot recall ever having a problem with sway nor did I every see a 5th wheel sway. I agree tires are important but IMHO there is something else going on to cause a sway. Either you are not level, and weight is too much to the rear, or the weight in the 5th wheel is unbalanced to the rear.
I also had Airlift 5000 on both vehicles to level the rig since generally pin weight will squat the truck a bit and can lead to the nose of the 5th wheel being down. While that could cause a sway issue too, that sway usually originates at the truck and not the end of the trailer.
I would be looking at the overall balance of the 5th wheel (are your tanks rear? that could cause an issue) and also looking at leveling the entire rig front to back before changing tires out and finding the problem never went away.
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2018 Greyhawk 29MVP-Sold
2023 Jeep Gladiator Mojave
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