As to your original question, the term you want is a "double single sprocket" or "double simplex sprocket". Like these:
Unfortunately, most often they seem to be typically available for ANSI #40 roller chain and larger, or British 06 chain (
which I doubt would match). (Some are in China, so there's the distribution problem as well.)
There's always custom fabrication—
these guys say they can make it—better still, find a sponsor to make it.
(In case you're wondering, these double single sprockets are used in some conveyor systems.)