You could be on to something there Jason. Here's a link to the Ohio BMV's
code:
Moped Information
The question of a motorized bike trailer isn't addressed by the Ohio BMV. I know they allow larger motorcycles to pull trailers and sell license plates for those trailers.
The fly in the ointment would be on operating in that 3 feet from the right edge of the road zone. I figured the one wheel trailer I sketched out would do it comfortably.....but the BMV's code states "one wheel ahead of the other in tamdem or two behind the one front as in a trike". With the big basket on the back of the trike that would offer the utility of a trailer.
I haven't been able to find out anything from BMV about it. I'm beginning to think I'd be better off installing saddle baskets like the paper boys use on the back of my bike and forgetting the trailer.