Perhaps you could make use of pre-made cardboard(white) boxes in addition to your current methods. One could place the art piece in said box(dimensions L12" W9" H2") which would be half filled with styrofoam packaging peanuts/material. The shipper should then fill the top portion of the box with styrofoam and then seal it shut.
You could also place your art piece in between 2 sheets of cardboard and then tape the cardboard shut. Perhaps you could make some sort of insignia which can be placed on the cardboard or box.