This came out all glittery:

Epoxy tinted with transparent black dye does a pretty good job of not obliterating the cracks between the cuboids. In person, the cracks seem less conspicuous around the borders of the glass pieces, but they’re visible enough for this ahem use case.
Under the proper lighting, a few bubbles appear along and above the black layer:

The new thing this time around were three pins holding the layers in alignment while the epoxy cured:

The conical end comes from grabbing an 8 mm snippet of 3/64 inch steel rod in a pin vise and twirling it against Mr Bench Grinder for a few seconds.
The pins pretty much dropped into 1.1 mm holes created while cutting the sheets. The tiny circles mark the laser path around the pin holes:

The “holes” in the top sheet (upper middle) are in the Tool 2 layer so they’re not cut, because it was easier to match-drill holes halfway into the top sheet with the drill press than to figure out how to convince the laser to not punch all the way through. Engraving (along the lines of the earring borders) might work, but I’m not sure how well a high-aspect-ratio hole will engrave.
The mirror sheet is reversed left-to-right in order to cut it from the back of the reflective layer. I’m not certain this is necessary, because acrylic is basically opaque to 10.6 µm IR light and any doubly attenuated reflected light will diverge strongly from the focus point at the top surface, but it’s the recommended procedure and easy enough to do.
The cork cuts with its adhesive layer up and blue tape on the bottom to prevent soot from accumulating in all the surface crevices.
The alignment pins worked surprisingly well:

The top sheet sticks out 0.3 mm on one side:

Oddly, there’s no place where the top sheet is indented by any noticeable amount, so there may be slight size differences depending on all the colors and ages in that stack of plastic sheets.
I’ll cure the next one top-side down, giving the bubbles an opportunity to rise toward the mirror layer and maybe become less conspicuous:

The tricky part: finding and arranging glass chunks within a 100 mm circle!
Avoiding narrow gaps and acute angles in the perimeter, as the notch on the left side, should simplify draining the epoxy.
This one certainly does look just … smashing!
Continuous process improvement … [grin]