I think you might be underestimating the total towed amount. Sure, the Elise is 2,000lbs, but you'll likely be looking at bringing a toolbox or two, an extra set of wheels/tires or two, maybe some fluids, etc. In the end you'll be really close if not over the 3,800lbs, and you are always better the further under that you can be.
There have been a couple good threads both here and on the other forum about tow vehicles. The best choice sounded like a TDI Toureg, but there are a lot of other SUV's with higher towing capacities. I know that the new Grand Cherokee is rated for 5,000lbs with the V6 and 7,400lbs with the V8.