I have a similar setup with a heavier TC (3,600 wet) and have just the upper stable loads and don't have the issues you describe. The truck should be similar (mine is a CCLB F350 diesel, 2013).
Here what I did to accommodate the camper and achieve a comfortable handling truck:
Upper stable loads
Sumo springs
Upgraded all shocks to Bilsteins
Added a sway bar (Fords OEM) which wasn't an option when I ordered the truck
Upgraded from the crappy Michelins to Nokian Rotiiva AT Plus tires rated to 3,750 pounds.
I have Fastguns and Talon frame mounts.
Does the truck feel different with the camper on? Of course, but after 20,000+ miles I am very comfortable with the way it handles. It did take a little getting used to (I clearly remember the first trips locally where I was still nervous about the whole set up). But today I am accustomed to the feel of the rig on and off road. The truck rides like a brick empty but that's the price of preparing for the load I put on her. I am about 800 pounds over my GVWR but under both front a rear axle ratings. Some would say I am over the GVWR and therefore unsafe. Everyone has an opinion - I am very happy with my choice.
