I don't know any of the specifics of your hitch/receiver combo but with a 1500 I assume you have a 2" receiver. With that, I assume you have a 2" shank on your hitch. I never had a problem with my 1500 and the 2" hitch shank I currently own (tongue weight approx. 1000 lbs.) - it was pretty tight and not an issue. Is the receiver a factory receiver? What hitch do you have? Maybe the tolerances of one or the other is not quite up to snuff? Anything loose?
When I moved to the HD truck I did have problems with movement in the receiver due to the adapter from 2 1/2 to 2". I solved it with a hitch clamp device but not like yours.
https://www.amazon.com/Hitch-Clamp-T...gateway&sr=8-5