One way to do it would be to use a short piece of wood/dowel in the hole you could glue a washer to the back. Then recess an area into the back of the panel that would allow the washer to sit in flush. As long as you get it lined up you can then just push the end of the wood/dowel to eject. The washer keeps the whole thing from falling out.
Great work, you're setting quite the pace.