I noticed these cheap Chinese LED array mini-panels recently and am experimenting with them as backlights for Lithophanes milled from Candlestone (similar to Corian). You can't apply to directly to the back of the panel because you get a concentrated square of light on the front viewing side.
You have to have a fairly significant air gap to make them work as a backlight. Wondering it there is some magic material (transparent plastic sheet of prisms(?) that you could use to diffuse the light so that the enclosure would be relatively thin?