"That sounds good, but that's only half the job. He still wants to do the non-black areas as well, which is the greater challenge."
Soo, enter idea #2. Take a separate board, cut out ALL shapes, but a little bit smaller. Cut the plexi-shapes the same size, to use as inlays.
Route out the shapes from the inside a bit bigger to create the overhang.
This way there would be small strips of unlighted areas between the lighted ones, but most of the area would be lit.
The only problem would be to attach this board to the side.