Re: 2000 F250 7.3
Not clear if the 675 lb. is the weight of your actual hitch (that's a HEAVY hitch if it's the one bolted to the truck) or the tongue weight of your trailer? Add the hitch weight of the (loaded) trailer to anything carried in the truck (passengers, too) and make sure it doesn't exceed the truck's payload capacity (GVW). Also, make sure that the trailer's total weight doesn't exceed the truck's total towing capacity(GCVW, different than GVW). For proper handling, make sure to keep 10-15% (15% is best) of the total trailer weight (when loaded) on the tongue.
I've been an RV'er for a long time; the truck looks like a good match. You will like the Diesel's torque and mileage, especially when towing. I have a Cummins/Allison power train in a 24,000 lb. motorhome. I get 11 MPG hwy and don't even notice hills. Diesel is the way to go in a heavy rig.