The tow rating is determined by the manufacturer taking many factors such as axles, tires, frame, brakes etc. They have a set of standards to abide by. I believe Ford still used the old SAE standards in '13. The 7500lbs was determined with an empty truck and 150lbs allowed for the driver. Any weight added to the truck will reduce the tow rating pound for pound. Your calculation of gcwr -gvwr would give you a lower number because he truck is loaded at max gvwr already.
The tow rating is usually the last rating to be concerned with as you will exceed other ratings, such as payload, first. Find your payload rating, subtract weight of all passengers and gear added to the truck. What is left can be used by the trailer tongue weight. Figure approx 13percent of loaded trailer weight as tongue weight to get an idea of trailer size.
Your hitch receiver should have 2 weight ratings as well. The 500lbs is for dead tongue weight. Above 500lbs you need a wd hitch, up to the max rating which is usually around double the dead weight or around 1k.