Random thoughts:

I've seen kids pass through a time when they could master shifting gears but were unreliable with hand brakes.

There's the Electra Townie 7D in 20" wheel (no front suspension).

Probably still too big, but years ago, Schiwnn, Raleigh, Gitane and others built small (24" wheel) kids' road bikes. Rare today, but they do occasionally show up on CL & ebay.

You could add a three- or five-speed hub gear to his present bicycle. Easy to shift, option to stay with a coaster brake, much less expensive than any other suggestion on this thread.

tcs