A quick review to help with being near the load limit on the F-350, in order of difficulty:
Stableload Quick Disconnects (they are relatively inexpensive and look easy to disengage and engage.)
Airbags (so the vehicle can go from a softer ride to stiff enough to take a TC without the headlights going skywards.)
Heavier duty front springs (if it doesn't already have them from the factory.)
Rickson 19.5 rims which would allow for heavier duty tires (load range H, I'm guessing, about 4900 pounds a tire.)
Since this is about addressing the weakest points in a chain, going with better rims/tires, a beefier suspension, and airbags will make the FAWR and RAWR the weakest points, and from what I read, the Ford's front axle is 6000 pounds, the rear is 7000 on a SRW model.
Of course none of this increases the manufacturer's weight rating, but this looks like it can make a borderline ride a lot more comfortable, especially when off-road.