Thanks for the replies.
The sprocket is an odd duck, the teeth fit well with the chain. I guess it's a scooter thing.
The sleeve bearing idea seems sound. 7/16-to-11mm, close enough. I'm hopeful that it won't crumple up in there under stress. If I get a steel finished-bore sprocket, maybe I can use its set screw/s in place of the key bit. I'll have to order the stuff up, the layouts on the mcmaster catalog page aren't detailed in that regard. I won't know till I know.
Here I was wondering about J-BWelding the original sprocket to another and....
Good.
I have to come up with a platform to mount the motor on, too. J-BWeld is not out of the running, yet. 
More challenges lay beyond.