Starting with vector based artwork will work the best when translating to laser cutters and 3d printers.  I used Adobe Illustrator to create my design.

Download the file below to get a feel for how it's all put together.  This file contains layers for the case as well as the runes and acrylic cut lines.

I played around in Adobe Illustrator until I had vector-based images of all 4 runes and a 5-sided outline for the edge of the acrylic.  The laser cutter software wants vector artwork only with no fills, just stroke outlines with different colors marking the different depths of the cut.  Red here is lines that will be shallowly etched, and blue is for cuts that go all the way through.  I made sure the red lines didn't actually cross anywhere since I just wanted the laser to go over each section once.

Print your design out on paper and wrap your neopixel strand around it.  Adjust your design so the corners fall neatly in line with the neopixel bend points -- you don't want to end up with a pixel stuck on a corner.  My design allows for two pixels on each of the faces on the upper left and right, and three pixels for the two lower faces.  (Note:  This is a 60/m neopixel strand -- I later used 144/m for the finished project.  I also ended up trimming off the ones along the top)

This design looks better when the runes are cut on the back of the acrylic, rather than the front -- it adds to the "floating in space" illusion.  To achieve this, remember to reflect the runes across a vertical axis, so they're backwards before cutting.  Then when you look at them through the acrylic they'll be oriented correctly.