I have a 2007 Edge with the factory trailer tow package. I tow a 16' Airstream Caravel (1965). The Airstream factory lists the weight of this trailer at 2200#, but I think that's optimistic. I added a couple hundred lbs when I restored it, and my guess is I'm closer to 2800#. I have had a problem towing when the temperature is over 80deg and i'm driving at 50-55mph. The air conditioning compressor shuts off. When I slow down, it comes back on. I am a Ford retiree, and I have talked to the trailer tow engineers at Ford about this problem. It would appear that the vehicle is sensing an out of spec condition (trans or engine oil temp or coolant temp?) and is turning off the compressor to lessen the load on the engine. The dealer says no problem with the AC and no engine codes. The engineer at Ford suggests that I am towing a trailer with too large a frontal area, which adds aerodynamic drag at highway speeds. So, I would suggest that you proceed with caution. It's too bad. I love the Edge, and it seems to tow the trailer effortlessly. I wonder if I have a sensor that is out of calibration that could be causing the AC to cut out prematurely, but I have no easy way to check this out. Oh well, it's a lease, so I guess I'll just have to get something else.
As for switching out the hitch, if you have the factory hitch, it is welded to the bumper beam. You would have to cut it off or replace the beam with a non-trailer tow beam.