I feel like saving 1 move in 10 (9 to 10 is 2 moves, 10 to 11 is back to 1 move) is not worth the mental capacity required to remember current up/down direction. Easier to let the muscles do the work and let your mind wonder.

That's a good point, though I do think that it's not that big of a mental hurdle. Consider knitting, for example.

That sounds similar to the concept of Gray code [0].

For electronic locks, there is a similar method that allows you to try a 4-digit code for each key press [1].

[0] https://en.wikipedia.org/wiki/Gray_code [1] http://alvaray.org/brute-forcing-pincode-keypads-using-combi...

Yup, that's the general idea I also had in mind.

Those "try all n in shortest combination" sequences are called De Bruijn sequences in general.

https://en.wikipedia.org/wiki/De_Bruijn_sequence

These codes have been used to break wireless garage door openers in comically little time: https://samy.pl/opensesame/

In practice 009 to 010 is a single move, because your thumb can cover and turn two or more wheels at once.