It is entirely possible that the airbags are hurting you way more than they are helping you. Air bags do absolutely NOTHING to distribute weight. In fact if you set up the hitch, and then level with the bags. You are changing the hitch setup, and in fact moving less weight to the front axle, and lost weight on the front axle means oversteering, and induces sway.
Try towing WITHOUT airing up the bags and see if it is better.
I tow a 30' TT, and have -0- / no hint of sway at any speed, which is as it should be.
Another thought, and don't laugh until you try it. Move your drivers seat closer to the steering wheel. Doing this will bend your arms more. That will give you more control, creating a more stable and lessen the chance of you being the cause of sway. Driving with you arms straighter makes it easier for you to unknowingly move the steering wheel. Doubt me. Take a look at the NASCAR drivers. Notice how close to the wheel they are. They are right up on it and some rest their elbow on the wheel in the turns. This is in sharp contrast to the way they sat years ago with their arms straightened out. They learned that the closer you are the more stable you drive.