Anti-sway bar(s) on the tow vehicle always help the ride, as do good (premium) shocks. I run Helwig sway bars front and rear and Bilstein shocks on our 2500HD. Anytime youupgrade the suspension/safety components of a tow vehicle, you are not wasting your money, and a rear sway bar is surprisingly affordable. Check out www.summitracing.com
Additionally, tire pressure on both the tow vehicle and the travel trailer is critical to proper handling. As is the suggestions of the folks above.
Have you cleaned the bar on youranti-sway device ? Do a search as to cleaning methods. As far as them being inadequate, I doubt that. I have been in a hurricane pulling a 28 ft bumper pull with a friction anti-sway bar and a good weight distribution hitch and haven't had any issues.
Granted our truck is a crew cab and has a longer wheel base, which makes it harder for the tail to wag the dog. However there areother factors that should be looked at first (air in tires, etc) before spending money.
As I mentioned, good/premium shockson the truck. The additional weight / lengthof the trailer can magnify shortcomings in components of the tow vehicle.
Additionally as the other folks said, you need to stay at 65 or belowwith the STdesignated tires, which may not be the best in the world (probably from China).
You should take microwave into the house and see how it functions inside so you can work out whetherthe problem is in the microwave or the trailer, as the folks above have suggested it could be.