Another solution would be to route the pixels as you did but the full thickness of the MDF, route the thickness of the plexiglass on the outside, fit plexiglass into that routed exterior and light everything from behind/the inside.
Another easier solution would be to make a hole as big as needed for the alien, route the exterior to the thickness of the plexiglass (doing an edge to put the plexiglass on) and cover the plexiglass with a vinyl (or something) with cutouts for the pixels.
Or even better, to go around the paint/thickness/doesn't-fit-anymore-when-I'm-done-painting-damnit problem, simple route the plexiglass pixels and also route the plexiglass like your template but in opaque plexi, same color as the side panels. Or heck, finish the whole sides with that opaque plexi if you can!
