Had a similar issue with a Rola storage box I added to my Roadtrek 2 years ago. Same idea, box mounted to the rear of the vehicle with a 2" hitch shank, into the 2" receiver on the class IV hitch. Noticed the wobble almost immediately upon leaving the point of purchase.
I just stopped at the first Walmart I saw (or any other hardware type store) and picked up some zinc plated flat washers of varying thickness because I wasn't sure what thickness I would need. The ones I got come in 1 3/8" outside diameter, and can be inserted down one side of the shank inside the receiver. Get someone to gently rock the ramp/platform for the scooter back and forth and slip one of the washers in between the shank and the receiver. I managed to get one in on the side (washer situated vertically). I had to tap it lightly with a flat blade screwdriver and hammer, to get it started and then it seated itself after some more coaxing. Then use a 10" or longer cable tie wrapped around the shank as close as possible to the receiver, to keep it from falling out. There may be better options for this issue.
Total cost, if I recall correctly, was around $0.09 for the zinc plated (stainless steel would also work) washer, and maybe a few cents for the cable tie?
No more wobbling storage box.
The hard part is getting a washer that will fit snugly, but that you can still insert with relative ease. I had to trial and error it twice before finding a good fit.
These will work
Washers