What your feeling could be a combination of many things. Including tires, shocks, and worn suspensions components. Having a stiffer sidewall a LT tire is going to give a better towing experience. Less squish equals better handling period. Like others have already said properly aired LT tires will still give a smooth ride. As for P metric tires on 1500 series trucks? So what? The manufacturers install tires that make the vehicle certified for a certain weight rating. They are not interested in towing as long as you do not exceed the vehicles GVWR.