The F350 was meant to carry a lot of weight, so I doubt that you will
ever get a Super Plush Ride.  You might check with the tire dealer and
see if changing to another brand will offer an improvement.  Yokohama
tires have the reputation of offering a smoother ride than many other
brands.

The side-to-side pitching is in my experience a trait of vehicles that
have a high center of gravity like your van.  You might lessen that
tendency by increasing the tire pressure, but that will reduce what
little soft ride you have.

The biggest improvement in ride on my F250 truck was when the bed was
full....the ride smoothed out wonderfully.  You might put a couple
hundered pounds over the rear wheels and see if that doesn't smooth the
ride a lot.