After some more experimenting I've put together a working worm gear mechanism with a 12:1 speed reduction. Here's the Instagram video of the model in action.
I tried a variety of different gear profiles before finally settling on the yellow one here.
I put together an almost two turn worm and a geared camshaft.
The two parts fit into a box with a cam follower.
I'll put together a download with this mechanism and probably another with a worm gear driving a crank rather than a cam. I have an idea for a snail model which could be based on this mech, you can see a sketch of it it in my Instagram stream.