Are you sure it's true sway? Not insulting your intelligence, just asking, here's why.
It took me a trip to Disney and back at around 60mph to finally figure out my issue. The whole rig became very unstable much above 60. I called it 'sway' because I felt like I was all over the road. In fact is wasn't a trailer issue at all but a hitch set up issue. I was running 1200lb spring bars assuming that was plenty. Only when I weighed it and saw I was at 1500lbs that I realized the problem. Purchased new bars and I've been fine since.
TT's 32ft and over can be a pain to dial in IMO. I think small issues become big issues when you're pulling 35ft behind the bumper.