A thought on sway (obviously from a noob to the forum, although not to towing)...
Could it be that the real issue isn't tongue weight, but the center of gravity of the trailer? When the trailer sways, it rotates about its center of gravity. If the center of gravity is near the trailer axle(s) the sway amplifies itself, but if the center of gravity is well forward of the axle(s) the sway cancels itself out. If this theory is right, shifting load forward in the trailer helps a little, but moving the trailer axles further back would help more (probably a manufacturer issue). Then, if the tongue weight is too heavy, use the WD hitch to take load off the rear of the TV.