On your two passes at the CAT scale, did you have your weight distribution hooked up when the trailer was connected on the 1st pass? If you did, then you did not get an accurate tongue weight measurement. The weight distribution hitch will transfer some weight back to the trailer axles in addition to the tow vehicles front axles.
If you can get your tongue weight up closer to 13-15% and it tows nice and steady with no traffic or wind but is just getting blown around you probably need a better hitch with integrated sway control or at least a 2nd friction bar. Better tires (LT) help as well.