C is for Cookie
As you probably know, It’s slightly more detailed as the mechanism for the balls touching is an interference from the donut. That is, the donut is placed slightly off center to “rock” the balls into position from the bottom. So, the center to center distance is just a starting point for the endeavor. Some of the donuts are actually placed ever-so-slightly off center to “push” the balls i to place. That’s why the donuts have to be adjusted.
I suspect I could (re)design the template to have the placement holes already off-center and then you could just place the donut at a specific spot with the edge of the donut touching the template at a single marked point. (Rather than placing the donuts in the center of the placement hole and then adjusting all that need it). The offset placement holes might reduce the number of donut moves. I’ll give that some thought, but likely not worth the effort. It’s pretty easy already.