With the Joggy Thing running in LinuxCNC 2.7, touching XY off on the fixture was trivially easy:

The pips are 100 mm apart at (-50,-50) and (+50,50). Astonishingly, the laser aligner batteries are in fine shape.
I should have protected the platter before drilling all those holes:

All’s well that ends well:

It looks even better in the dark, although you’d never know it from this picture:

I wish I could engrave those patterns on already-drilled platters, but dragging a diamond point into a hole can’t possibly end well. I could deploy the Tiny Sandblaster with a vinyl mask, if I had enough artistic eptitude to lay out a good-looking mask.