I see your point about the weight. Don't know about that.
What i had imagined was to flip the carrier, mount it to a sheet of plywood and have it mounted closer to the car. Then attach a sheet of coroplast to the back side and have it follow the curve of the template.
The wheels could have coroplast covers as well simply by flexing it and attaching it to the frame.
It would improve your aerodynamics greatly and pay for itself easily!