towing my now Ex Wildwood 31BKIS with the same truck as you I was never able to get that darn thing tow stop dancing around even after weighing it wet, moving stuff around and playing with the Dual cam Reese hitch I had. Made the jump to a Propride 3P and never looked back after that. Sway was a non-issue after using that hitch. I've moved on to a fifth-wheel in the last week or so its no longer a concern for me.
My advise is to go to a Hensley or Propride hitch. Other will suggest moving weight around, setting up your hitch different and such, it may or may not work, but guaranteed a new Propride/Hensley will 100% satisfy your issues. I'll never tow a bumper pull without one now.