The max I personally would tow if I owned that truck would be a dual 3500 lb axle rig which probably has a gvwr of in the 7600 range.
However I would never buy that truck with the intention of towing that trailer, that is only if I had the truck first and that would be what I would personally set the limit at on the trailer. If I had a 7600 lb trailer and was shopping for a truck I would get a gas 3/4 ton.
But there are various ratings that you are already aware of that may or may not be exceeded in towing a 7600 lb trailer.