I have personally experienced this in a flat trailer loaded with wood. The trailer had no brakes, which in my opinion would have saved the day.
My load on the trailer caused the whole unit to float. Little to no weight on the hitch. I was much younger before the incident and grew many years older once everything calmed down.
I reached a speed of 45 miles per hour and it started to sway. The sway increased in intensity and osculation until I was basically holding on for life. Traffic backed way down and allowed me enough room to cross both lanes. taking my foot off the accelerator it slowed down in time to not dump the load or me and the truck. I said my prayers after that.
I never wish to experience that again let alone with a TT and the weight that is potentially thrown around.
When it begins just tap the brake controller to slow down the whole rig and allow the TV to pull it all straight again. No need to accelerate, just let the momentum of the TV pull it all straight with the brakes on the trailer.
I hope this helps. Also test your brake controller every trip. make sure it functions as needed before you put to many miles on it from home.