I have a very similar issue with the mobility scooter carrier on my old pickup. The carrier has a mount for a license plate which would be visible if not carrying the scooter. With the scooter on, the plate would face toward the ground.
When I turned in my regular plates for my disabled vet plates there was a Dept of Public Safety Officer there and I asked him which would be the place to mount and he said just go with the regular mount on the pickup. He said it does give a cop a reason to pull you over but in his words "There are a million other reasons".
I suspect the same is true for any type of vehicle. Or Cop.