[frizzen]

I'm not 100% sure on your design of that last piece, but think i've got a basic enough idea.

Instead of doing a full redesign for the bi-stable latch I might try to file some directional ramps on the lower side of the plungers 'paddle looking section' to help them ease into next position. Then cross-drill the plunger shaft for a pin near the coupling sleeve maybe like 45 degrees out of phase with the paddle, so that at weight-released full-down it can act against a couple bumps on the collar to start rotation to advance next position?

If it still doesn't want to advance, you might be able to mill a zigzag path in plunger shaft, then a pin in the collar rides in zigzag to keep it moving.

I dunno, worst case you could take apart some 'pop-up bathtub drains' for some other design ideas.