If you want the diesel 6.7, then I would suggest going to a higher GVWR F350. It won't cost that much more, and the ride is not much different. It is the diesel engine that is using up the GVWR.
Yes, many just add airbags to the 250, and with heavier rated tires and wheels, this will work.
My 13 F250 6.2 gas was ordered with heavier suspension, and has a good payload. With 4.30 gears, it is rated to tow a 15,300# FW. I would not want to carry a much heavier loaded FW, than say 12,500.
My truck rides really well, but you do know when you hit a large hole, or rough railroad tracks.
Jerry