Modest progress on the box body. But at least I got the new lid inlay cut. I used a home-made fractal design to avoid the pesky copyright uncertainty and to find out how detailed such an inlay can be made.
The new piece of cherry was less brittle but I believe what made a major difference was to soak the inlay blank surface with ample thin CA glue (and a whiff of accelerator spray after that). It reduces the tendency to fuzz and stabilized the tiny protruding slivers somewhat. I also used the even sharper 1/8" version of the Kyocera 30-degree bit. Total machine time for both pieces was about 55 minutes.