Having found a handful of popsicle sticks on my desk, I had to finish this up:
The fixture has the same layout as the craft stick version, sized to fit the smaller sticks. They’re a bit thicker than the chipboard sheet, but match up well enough for the purpose.
Even though the sticks don’t have much room for cutout letters, I had to try it anyway:
Aligning the template to the fixture uses LightBurn’s Print-and-Cut tool, which seems easier than nailing the fixture to the laser platform.
I suppose if they ever make actual popsicles with wood handles, they can tell who gets which one.
For whatever it’s worth, the larger craft stick markers in the garden remain in good shape.
The Smell of Molten Projects in the Morning 
Preschools and Kindergarten love popsicle sticks with names on it. If you have a snack, move the popsicle stick with your name, if you go to the bathroom, the popsicle stick will mark your absence from the room (like the Weasley clock, but for a whole group).