I was initially towing without a W/D hitch because my truck was capable of doing so. However the ride was much like you describe which led me to buy an Andersen no sway no bounce hitch. The difference was huge! Not sure if other W/D hitches do as much as the Andersen for bounce.
Also, you may want to check out the sticky at the top of this (TT) forum regarding the Dexter HD suspension. I just finished reading the whole thing and it sounds like many people say it significantly improves the ride. Personally after reading that thread, I'm sold on it and it will be the next upgrade on my TT, definitely before our long trip this summer.