First, do you really have sway? Some people think that any sort of motion from the trailer is "sway" when it is just an unavoidable bobble caused by uneven road surfaces. When the trailer starts whipping back and forth uncontrollably, forcing you to hit the trailer brakes, THAT is sway. When the trailer just moves a little and goes right back behind the truck, that is not sway.
There are other behaviors such as push-pull (side-side motion) from passing traffic, and porpoising (up-down motion) due to uneven road conditions, that also may be mistaken for sway. Push-pull and porpoising are issues that can be helped by proper adjustment of tire pressures, your weight-distributing hitch and/or upgrading to a hitch with integrated sway control.
Squirrelly or floaty steering is also not sway. It is an indication of too little weight on your front tires, which means your weight distributing hitch needs adjustment.
Second, do you have an "equalizer bar setup" meaning a generic weight-distributing hitch, or do you have the EQUAL-I-ZER *BRAND* weight-distributing hitch with built-in sway control?
Third, which "key stone KZ290" do you have? I tried to look it up and there are no less than three different models by Keystone with KZ and 290 in their names, and neither of them are KZ290. There's a "KZ Sportsman 290 RLS" and a "KZ Spree 290 BHS" and the current "KZ Sportsmen S290RL".
The current S290RL has a GVWR of 8000lbs, a dry weight of 6260lbs, and a dry tongue weight of 790lbs. This should be well within the capability of an F250 diesel, and there is no way it's lifting too much weight off the front end of the truck with that big heavy diesel engine.