Sway bars are on a vehicle and used to control roll. On a trailer, you have torsion or spring bars, and friction sway control. Having the Fastway E2, you do have spring bars with some sway control built in (Not as good as the Equal-I-Zer E4).
I would first make sure your setup is correct. Make sure you have the proper sized spring bars for your application. Make sure your hitch head is adusted and you set up the hit per the manufacturers instructions. If you are still having issues, head on to the scares and see if something is out of wack (IE Low tongue weight, or not enough weight distribution.) One thing I did was drill a hole in my shank as close as I could to the tow vehicle. Even a few less inches closer with the ball helps with leverage.
And, I think you will always feel some wind. My DGF father drives coach busses, and he says he can feel wind and tractor trailers.
EDIT: Looking at your floorplan, your fiction dry weights look very light on the nose. And, that floorplan looks like you can easily load too much weight behind the axles.
Also, make sure your tires are aired up properly on both the trailer and TV.