On the sway bar issue, you may not need a whole new sway bar.
First, try replacing the factory soft rubber sway bar bushings with stiff polyurethane bushings from Energy Suspension or Prothane, among others.
I replaced the factory rubber bushings of both front and rear sway bars for both my F350's, as well as the front axle transverse tracking arm bushings with polyurethane and the bushings made a world of difference. I had no need to go to larger aftermarket bars, once I got good bushings in there.
My F350SRW hauled 4000 lbs in the bed for 5 years straight, no sway to speak of, for a single rear wheel truck. Of course I had other mods too: super heavy duty rear spring packs, 285-E tires, heavy duty rear wheels and Bilsteins all around.