Probably not saying anything new here.
We have pulled a couple tent trailers (aka pop ups) with our Jeeps. (JK, TJ and WJ) We stayed within both the hitch weight and the trailer weight requirements. One of my coworkers pulled a Forest River 1640LTD with his TJ. Specs show a hitch weight of 162 and UVW of 1465. He loved the trailer and had the unit with the extra height for going off road on some "easy" trails. For "myself" those are about the max weights I would go because they are dry weights and do not include gear, propane, water or a battery. All putting you closer to the Jeeps recommended tow ratings. We pulled an old tent trailer a number of times with a JK 2 door. I had trouble eliminating the sway even though I felt I had the weight positioned correctly in the trailer and the tongue weight at about 12-14% of the trailer weight. We ended up with a new, slightly heavier trailer where I felt the mfg. was not even close to being correct on the tongue weight. They listed 190lbs on the tongue but when I weighed the tongue with the propane tanks and a battery, it was actually 320lbs and way over what I could handle with our JK 2 door. Ended up with a new tow vehicle. Like AMS417 says, look for a 8 foot box (usually a 12" tent trailer). Somewhere around 1000 to 1400lbs and then do an accurate tongue weight check to make sure your are under 200lbs.
Sorry, guess you asked more about the transmission. While our TJ has the 42RLE our WJ had the 42RE. I agree with you. - Overdrive off and not overworking the TJ on the hills and you should be fine. Just staying within the TJ specs and taking it easy.