I run 19.5's as well and am under 15,000 lbs with a rear engine. After reading all of the above and what you have done adjusting tire prissures, I am convinced that it is not the tires and further tire adjustments will be chasing a ghost.
I am also convince, including some experience of my own, that it is worn bushing and/or alignment issues. Loose connection points due to worn bushings will cause all kinds of problems. When you take it in, have them check the entire suspensioin system. It wasn't designed to do that so something is out whack other than tires.