Sway like trailer would just take off on it's own with no/minimal input that would make it sway? Like have to use the trailer brakes to pull it back in line?
IMO, that heavy of tongue weight and light in the @ss end since you aren't hauling heavy toys in it, "should" add to the stability.
Sorry to hear this, but before spending big bucks on a new hitch, maybe analyze what kind of "sway" you were getting and what your past experience and expectations are for comparison to the current experience toeing this trailer.