Yes moving the hitch will give you one inch, and still have 6" between the tailgate and trailer, so that part is good.
I have heard that you do not want to be less than 6".
IT is really something to think about before buying a 4X4 F-350. I am thinking of getting a 2 WD for that reason, I want to be able to see over the pickup bed! I will not get any 'fancy bling' such as the 20" tires. I enjoy the vibration absorption of the balloon tires. The dealership manager that ordered the 20" tire option was not considerate of your ride long term. 20" rims will make the truck feel like it is on rails as you go around a corner at 30 MPH, but a balloon tire will absorb potholes much better, without transmitting nearly as much vibration into the truck.
Good luck!
Fred.