it's been done before. i've seen it. but this is my stab at it.
helped with this, converting my end raster to vector, and doing the actual printing and dithering settings.
original sketch and lettering by Mizzyam.
inked and prepared for badge printing by me.

the one on the left has a little something special i'm putting in another submission momentarily- the surface-mount micro-LED from a cell phone sceen backlight, powered by a CR2032 will make this badge glow all around the outline and edges.