Just got the Cooper AT3's in 30 x 9.5 for my stock Cherokee and they worked great for me on mud, dirty steep hills, going over large rocks, etc. also quiet on the road. Only issue I noticed is some bumping in the rear if I was driving a little fast on gravel roads with potholes. This was with my hatch area full of gear so extra weight, and my shocks are original at 120,000 miles. Also noticed my rear bump stops are gone, so perhaps this is the problem (?) since these are slightly taller tires.
The stock shocks were never good when new, and they wear out by 30K to 40K miles. So your shocks are completely useless. I suggest get some Monroe Sensitrac shocks ASAP.
The stock rear springs are often wearing out by 30K to 50K depending on use. At your mileage, and with worn out shocks, and no bumpstops, you're rear springs are probably ruined. I think you need new rear springs. Get Crown (like Quadratec sells) if you want stock replacements. Crown parts are excellent quality and prices IME. If you want an even better spring and a slight lift, get OME springs.
Obviously having no bump-stops, worn out shocks, probably shot rear springs, and cargo weight is your problem.
I have some new bump-stops front and rear that I'll mail you for free, if you pay for postage. I MIGHT have some used, slightly worn, but still in fairly good shape, FREE rear stock tow package springs I can give you. If my cousing hasn't already grabbed them from my parts pile for his mother-in-law's XJ.