I had the same hitch, Curt Q20. I've had it on a bolted down ISR frame, B&W turnover ball, and Ram factory puck system. It did the same thing as yours. I put a 5th Airborne pin box on the 5th and that dampened the up and down slop.
I needed a lighter hitch after buying a cabover. I bought a PullRite SuperLite and stopped all that.
I think all the clearances in the Curt, and probably most conventional hitches, have what is called "clearance stack up". Given certain circumstances, all the clearances in the hitch system add up to produce those unwanted results.
PullRite SuperLite or Andersen will help a lot. I went with the SuperLight mostly because it was $100 less than Andersen. But it is also steel vs. the Andersen aluminum, if that makes a difference to you.