What's MOST important in that situation is that you ***STAY OFF*** the tow vehicle's brakes.
Whether you step on the gas or simply let up and coast, is up to you.
You are not really slowing down if you simply let off the gas. You will coast at your current speed for a ways.
Unfortunately for all we know, your sway incident was unavoidable. Even if everything is "just right" there are conditions and situations that will cause sway.
You are on the high end of your truck's capacity, but if you are happy with how it performs aside from the one sway incident, I would not bother upgrading the truck. Get yourself an Equal-i-zer or one of the DualCam style WD hitches, toss the friction bars in the scrap pile, and go camping!