I towed a Ford Contour on a tow dolly (1/2 of a car carrier that only carries the front wheels) from Houston to Knoxville (about 1,000 miles) with my Sport Trac with no problems. Even a nail in a tire didn't cause any more drama than a loose feeling in the back as I continued through a freeway interchange until I could get it stopped and fixed. As long as you stay within the rated tow limits, you should be fine. Adding a regular tow hitch to your Trac will help as well instead of using a trailer ball in the bumper like I did. And everyone else will rent to us without a problem. Go find a different rental agency.
The problem with the Explorers was more related to overloading and low tire pressure. I don't think I remember a single Explorer accident where the Explorer in question wasn't both overloaded AND had low tire pressure. Keep good tires on it (I like Michelins), check the inflation regularly, keep it maintained, and it will work just fine. Some here will add that you should change the shocks and add a stronger rear sway bar to improve handling. The factory shocks are pretty limp to make it ride soft, but better shocks will give better control. If it's a 2004 it probably needs new shocks by now anyway.
We have 96,000 miles on our 2003. It runs fine. I wouldn't have a problem jumping in and heading to Knoxville right now.