I also had an RBW hitch at one time. It was a slide bar type, that worked good. Yes, it was noisy/sloppy, very entry level. I would not go to all the work of installing the puck system, then an adapter, only to put a low end hitch on the adapter.
The adapter will raise the hitch higher, may make your FW tow more nose high.
I know money can be an issue for all of us, but if you can find a way to upgrade to a better hitch, you will be glad you did. I gave my RBW away, and bought a quality hitch, when I bought my new truck.
Any hitch that will fasten direct to the pucks, will be much better than the original plan.
Jerry