Just for some real numbers: I have Ram 5500 crew, 60" CA, diesel, 4wd that weighs under 11,000 lbs GVW with a GVWR of 19,000 lbs. If you go with the 84" CA, the GVWR is 19,500 lbs. So even with a heavy steel bed with six boxes and two hitches, I have 8000 lbs of payload remaining. Other than the pin weight of the fifth wheel toy hauler, what else were you planning on carrying on/in the truck requiring Class 6 payloads? I'm typically over 18,000 lbs GVW and 26,000 lbs GCW with no sagging issues or handling problems.
My rear deck height is about 3.5' high running 31" tall 19.5" with tires, rims and the 4wd suspension. I'm not sure how my deck compares to something 35" tall tires on 22.5" rims. You may have issues running a hitch low enough and may need to have it inset between the rails.
The F550 will be similarly capable with the same options but may be about 500 lbs heavier than my 5500 if equipped with the same rear upfit.
**After I posted, I see you plan on carrying large quantities of fluids. This can get heavy based on your requirements. You'll have to do the math to see if what I posted is insufficient in the lower class payload.