I have been thinking about this since you posted and I had an idea that might be better than simply meshing 2 sprockets as if they were gears. I know that sourcing gears is more difficult that sprockets.
I think that if you mesh 2 sprockets together it will be very noisy and wear out quite fast.
I don't know if there are gotchas with this idea.
But maybe this would be ok for a low power application.
What I was thinking is perhaps you could use a standard sprocket as the driver, and then select a size of sprocket for your driven that an appropriate chain could wrap all the way around (ie an even number of teeth???).
Then grind the teeth on the driven sprocket completely off or almost completely off, wrap your chain around the resulting disk and weld the *******s together.
If my logic is sound you should end up with a sprocket meshed to chain links that will rotate the jack shaft in the opposite direction, because the sprocket is designed to work with a chain it should last longer and be quieter than simply meshing 2 sprockets as if they were gears.
Just a random idea, at your own risk etc, etc