What type of material are you wanting to make this out of? Most of the gears you've made have been thin material, non wood. I am super cheap myself so when i can find a substitute for something or a cheap resource i try it.
Rather then going and buying a sheet of (whatever) from your source why not go down to your local Habitat store. I needed some double insulated glass for a solar hot water heater and instead of going to the glass store and buying the size i needed for over $100.00 I just went down to the Habitat store and bought a donated screen door with the glass for $10.00. They get donated flat material sometimes that they don't even know what it is.
Have you thought of using .25" corian for some of these gears? I think that would be a good material to make the gears from don't you? Why not go to a countertop company and offer to make a lithopane (let him hang it in his window at home instead of electrifying it) in exchange for some scraps. Could you make gears from .5" corian?
Have I solved your material problem now? I hope so because i want to see this crazy design you are conjuring up