That diagram has a lot of the concept right, though in this case, the Peachy can theoretically get in its own way... However, looking at it diagrammed out, I see that the only way it can actually hit itself with the laser is if it misses the object many, many times. Also, in that configuration, the sweep of the laser has to be precisely aligned in both axes to form a coherent line. If the laser is above the box, then it can scan across the part, only worrying about being perpendicular to one pair of mirrors at a time.

I haven't built anything out yet, though I've done a little bit of work with crazy "infinite mirror" boxes before.