I finally managed to whack the mini-lathe’s carriage stop handle with the chuck, prompting a quick repair:

I probably should have epoxied a rod into the recess under the handle, seated in a drilled hole into the hub, but let’s see how long this quick-n-dirty version lasts.
While I had the hood up epoxy was curing, I lasered a block of edge-lit acrylic to replace the credit card shims:

Which turned out to be one itsy too thick. Rather than sand / machine it down, the step over on the left grew a little brass shim:

Both pieces depend on snippets of adhesive sheet to hold them in place, which seems reasonable because they’re always in compression. That also eliminates the hole and pin I originally thought would be necessary; living in the future is just grand.
Thing looks like it grew there:

The orange stripe on the handle is laser-safe PSA vinyl.
That was easy …