This is a re-creation of Feyda's design from scratch, but staying as true to the original design as possible. Their file had a lot of excess geometry, and was "messy". This version is clean and manifold, and should print much smoother without all the extra vertices.

UPDATE: I've also added a "Lid Support Full" as a single, printable object with two of the lid supports connected, and an indent/ridge on the top to hold in place a card/paper/etc as it may be useful while playing. Obviously this version doesn't fit inside the box, but I thought I would upload it just in case it was useful to anyone.