Yes, I talked to a fellow at etrailer.com (VERY good & helpful seller, BTW) and he said the adaptor would tend to result in the trailer “really rattling around” in back. They sell the adaptors, but do not recommend them.
In the long run, since the hitch itself looks plenty good for Class III loads, what I may look into is whether some local shop can fabricate a “strong” Class II ball mount with 8” of drop. (8” should be “enough” to be “almost level” with the pop-up, and should also be a good compromise for our johnboat & utility trailers, too.
So weld a bead around where the adapter connects to your drop hitch - replace the 5/8" pin with a 5/8" bolt and locking nut as well. No more rattling but you may indeed have a torque problem if your Class II receiver is lightweight.
If you require electric brakes, perhaps you do need a Class III?