If I may suggest a way to potentially implement the ticking (for exhaustive purposes :D) You could have the simulation tick with every "turn move". That might make it a bit easier to plan out level to level, instead of leaving some of it up to chance, making it 100% deterministic as well. Essentially a time step happens with one key press (and a cooldown of .5 s between allowed keypresses to avoid player errors). I could really feel the vibe you might have been going for, seeing the gears move with the atom getting close and closer.
Although we weren't able to implement the set rotation concept, we did release a patch that adjusted some of the hit-boxes as well as include clock hands that indicate which level you are on (as they get closer towards midnight). If you get a chance to play again would love to see what your thoughts are on the patch!