Thanks gizmo, my guess that the engine sprocket drove the 12 tooth was wrong, it drives the 23 tooth that is behind the 12 tooth. The 12 tooth drives the clutch and the drum. That means the 12 tooth is a driving sprocket, not a driven sprocket, so having fewer teeth on it slows down whatever it is driving.
If you fit the NZ sprocket, and it has 23 teeth on the back and 10 teeth on the front, you will slow the drum by 17% without having any effect on the reel speed. That sounds like exactly what you want. Imagine it, the NZ guys actually fixed Victa's mess-up and made their mower work better than when Victa made it. We may have to suppress this information, or the NZers will become insufferable.