I think I finally got to a working design.
I decided to take a page from how my reloading press works with its rotary mechanism and make the same thing myself.
This saves all sorts of machinery to make it work, and substitutes, well, me. I don’t think the limiting factor is going to be me, and I don’t mind driving the press for hours at a time, so this might be equally relaxing.
The blank lump on top is the detent mechanism. Inside is a ball bearing with a spring to provide tension to make the stops more positive. On the bottom plate (which you can see though the nearest hole) there are divots where the ball bearing can live.