Your GVWR is for a fully loaded Edge. Hopefully you wouldn't be carrying 4 or more passengers in the car while towing it
, or say 600 lbs. of equivalent "stuff". You could just run your Edge over a State highway or other commercial scales, loaded as it would be when towed, to define your actual towbar load. That's more important, given it is lower than your 10,000lb coach tow capacity.
Our Monty Rae easily handles our 4300 lb Explorer, Pearl, via a Roadmaster Falcon All-terrain towbar.
Joel