A bit of tinkering suggested I needed a way to repeatably position stock sheets on the honeycomb, so I conjured stops that would be slightly taller than the magnetic spikes:
Three of those form a corner into which you can tuck victims of the same general size:
Those pointy MDF spikes should start with slightly rounded tops, because that’s what they’ll look like after a few uses:
I also made a low-profile stop for victims lying directly on the honeycomb for engraving:
The SVG images include a nested version to tile across random MDF leftovers.
The SVG images as a GitHub Gist:
The Smell of Molten Projects in the Morning 
Three large diameter neodymium magnets also make handy and very secure stops for use directly on the honeycomb. They are also generally useful for flattening out slightly warped stock from the corners, as long as you are confident you can avoid lasing them.
Maybe the 3 mm plywood and MDF sheets will remain as un-warped as when they arrived, but they’re now in the same basement with everything else.
I have some ferocious neo bar magnets (polarized through their flat side, not their length) that should hold the corners down; with my luck, through, the middle of the sheet will warp upward.
Then you can flip them over…