re: Box (trial run)

You can spray glue felt to some cereal box cardboard that has a loose fit. Wrap about 1/4" over the edge and get it to do a snug slide in fit such that the felt compresses on the edges but doesn't buckle. Usually this is enough to keep it down in place (easy to fish out and replace). You can also put some DS tape in the center to keep it flush.

Next you should try and place some small supports in the corners to fit a lift out tray! 🤠