I've towed numerous motorcycles and fourwheelers on various trailers with my two-door Wrangler and it works fine. It isn't fast and doesn't get very good mileage, but it gets the job done. The two-door has a lower tongue weight than the four-door due to the shorter wheelbase, but the shorter tow vehicle to trailer ratio is nice.
There was just a Wrangler thread here somewhere started by SwingLo, but the gist of all of us Wrangler owners' comments was that they are incredibly fun vehicles and something you have to own at some point. My wife and I have put more miles on ours than any other car we've owned. We have put close to 2,000 on it towing pretty Italian motorcycles back from Ohio in the last month, actually.
With that said, I don't know how well an Elise on a U-Haul trailer would work. Those U-Haul trailers are heavy. Are you sure about those numbers? You seem to have something crossed up. Their car haulers are much heavier than 750lbs. What you really want is a nice light aluminum trailer like a Trailex.
Actually, I just looked it up and the U-Haul car trailer weighs 2,210lbs: U-Haul: Equipment specs
. The tongue weight of the trailer might be 750lbs (though I don't see that spec listed), but tongue weight and total weight are completely different things. The Jeep is rated for 350lbs of tongue weight, and for pulling a max of 3,500lbs overall. The U-Haul car hauler exceeds the tongue weight, and would only leave 1,285lbs for payload capacity. Not going to work at all, and they wouldn't rent one to you.
Still get the Jeep, but rent a U-Haul pickup to tow the car and trailer to the track.