Hmmmnice.
It works as expected, and the kinematics reduce the mvement by a factor of ~3, so every Division moves the center by ~3 um.
Should be just about ok, meaning that the piezo can do the rest of the Z travel.
Issue is that I now need to constrain the ball on the micrometer, which means that I either have to grind a cup in the micrometer shaft or buy a different micrometer with a rounded tip to take the ball out entirely.
...maybe I should build a dremel tool mount for the lathe.