The class V hitch on fords state over 500 lbs tongue weight requires a wdh. His trailer has over 500 lbs tongue weight.
As stated above, you need to weigh your set up. Ideal tongue weight is 13-15% of loaded trailer weight. When you check your wdh set up, you want your front axle to weigh as close to unloaded weight as possible without going heavier.
Now lets talk about what you are feeling. True sway is side to side oscillations increasing in speed and size. Is that what you are getting? Are you getting some tail wiggle? Or are you getting front to rear porpoising? Each of these conditions are fixed a little differently but in the end it all boils down to weights, wdh set up and proper tire inflation. What are you running your truck and trailer tires at? Trailer tires should be inflated to max cold psi. Truck LT E tires are usually pretty good around 65-70 in front and 75 in rear depending on what your tires are rated for.
Does your wdh have integrated sway control? if not I would switch to equal-i-zer 4 point hitch or reese dual cam. Either will suit you fine. equal-i-zer is easier to adjust than the reese.