Tbf I think this is a tall order for someone who has never thought deeply about game design, I think something pretty cool could emerge from just a little bit of collaboration with a good game designer, or just putting a lot more thought and playtesting into it!
Maybe someone here should reach out and offer? Seems to have been lots of posts lately by people who are between gigs
Somewhat reminds me Eucledia the game that tries to teach mathametical construction.
But gamification is it's own art and science.