The potential payload of the F-550 would likely be quite useful to you. (You might be able to keep things super-light and use a F-350, but, this would require a lot of careful choices.) The configuration and options chosen can make a huge difference. You'll probably want to look at the crew-cab with 84" CA (cab to axle) rather than the crew-cab with 60" CA.
Keep in mind that this truck will be at least a couple of feet longer than a CCLB pickup truck. (Much bigger than a standard parking space!
Contact Duramag and ask about how long a flatbed they would make for it.

Aluminum Flatbed Truck Bodies and Beds - DuraMag Bodies
Flatbed Aluminum Truck Bodies from Duramag

The 2017+ F-550/450/350 cab and chassis trucks are c-channel aft of the cab, BUT, are much more rigid than older trucks. Torsional rigidity is EIGHT TIMES greater than that of the previous generation.
Bolt on a flatbed as you wanted (to "complete" the vehicle) and build your camper to go on it. Yes, you can overhang the rear with the right flatbed and loading the overhang lightly (camper open space for meals, flip down bunks, ...). Just be aware that the longer the overhang, the more the camper will turn like a schoolbus.