Silverado 1500, my recent experience

Long ago I replaced the original p-rated tires tires on my 1500 with LT tires (Toyo Open Country A/T). I was going to get load range C, but the max weight ratings for the LT load range C tires were less than that of the equivalent P-rated tires and was worried about overloading them. Therefore, I went with an LT load range D. The carrying capacity of those tires was greater than the axel rating on the truck. I've never regretted that decision. Like your experience, those tires solidified the ride when hauling or towing. No more tire squat or wiggle. Not only that, but I've currently got over 85K miless on those tires. They're ready to be replaced, but I've got way more life out of them than expected. That simple upgrade was one of the best decisions I made.
Some say that the Load range D are overkill and you're paying more per/tire, but at 85,000 miles and never a problem, I think I got my $ worth.