UPDATE: This was an early attempt never fully completed. Newer version with a few improvements - less "false sets", more secure teeth and deeper embossing on top and bottom faces.

Functioning Hellraiser Puzzle Box (The Lament configuration - art by artist064)

Print at 0.2mm (at least the core - it is designed to produce a 1-layer gap between the ring gears and is sensitive to layer height) and separate ring gears with a sharpened spatula, flat razor blade scraper, box cutter or similar. Print parts A and B separately (around 13 hours each). Ease the core (wider tabs first, careful of orientation and alignment of the narrow tabs) into the end of the "claw", they will need to flex a little.

I'd also recommend "breaking in" the core by giving it 5 minutes on a drill or Dremel tool to spin the gears. They will be quite stiff at first but soon wear in to move freely. Similarly the sliding parts might need a light sanding or at least operated back and forth a bit to loosen them up.

TinkerCad was used for the final intersection (subtract the negative from the artwork cube) as everything else I tried crashed or made a mess of the mesh. Eventually I discovered the Inkscape's Flatten Bezziers extension which was a marked improvement. I prefer to indent the stencil art as it preserves most visual detail when slicing for FDM. I'm thinking of painting gold followed by sanding back the raised edges. I've included the negative in case anyone would like to try their own designs.

A rough calculation shows the teeth should align every 224.25 turns of the dial (around 3.25 turns of the "slow" gear), though there are many "false sets".