We have only been in the class A world for a few years after 3 decades of towing TTs, 5ers, and toyhaulers. Every time we got new tires for our tow vehicle, regardless of brand, whatever we were towing was swaying all over the road, found we had to break them in as LT tires are made of very hard rubber. To alleviate this issue we ended up buying 2 tires at a time and putting them on front axle for a few months to break them in, then went back and got the second set and rotated the now broken in front tires to the rear. No more issues with sway or rear traction with broken in tires, our HD truck was dedicated to towing our rigs and just sat in garage when we were not out RVing.
The class A we purchased a couple of years ago had a set of Toyos roughly 10 years old although they showed very little wear, private seller dropped price $3K and we drove our new to us rig back home nearly 1K miles through blistering record setting TX heat. It drove great, tires being well broken in and scorching heat kept us glued to the road, got home and replaced with the same Toyos M154.
First time out on highway were were all over the place, checked pressure and tire store had them at max psi, prior Toyos only had roughly 85/90 psi. Dropped psi in new Toyo tires to around 90 and drivability improved dramatically, after a couple of in-state trips they are now broken in and riding marvelously.