Jeff,
I've been feeling my way through setting up my truck with a AF990 which is a little heavier than what you are working with (about 4000#). I've got a 2008 2500HD 6.0 CC LB(yes, the weight police will most certainly have something to say). I ordered it new with HD towing and HD camper package. I up-sized my tires to 3750# tires to handle the extra rear axle weight. With the original tires ( I believe were 3175#) it felt a slight bit uncomfortable but not scary. I also added AirLift 5000 air springs. I first put about 40# of air in the springs which made the rig feel uncomfortable and quite scary. I then dropped the air pressure down (19#) letting the overloads just touch which made a world of difference. It really feels stable now.
You've got a 4x4. They are sprung stiffer. Are your overload springs making contact. You can check if engaging the overloads earlier will help by jacking the camper up, putting some kind of spacer between the overload and regular spring pack. Take it around the block and if it feels a lot better you may want to look at some Stable-Loads.
Engaging my overload springs (with the air bags) made such a big difference in sway, I'm thinking about adding Stable-loads to make them engage even earlier.
In addition, my HD camper package included a HD sway bars. So this may have a lot to do with my rig feeling stable. You may be able to pick up a used one from a salvage yard at a reasonable price, most of the after market bars (that I've seen)are >$300.
It's very frustrating to have to keep spend money at "guessing" what might correct the problem.
Hopefully someone on here will have had the same equipment with similar issues.
Good Luck