I finally had some time to make it over to the local TAP Plastics and pick up the 1/8" acrylic sheets needed for the sides and rear panels. Since the only holes in these sheets are for the screws to mount into the vertical wood beams, it did not make sense to laser cut them.

Here is a photo showing the progress. You can't really tell but there is an acrylic panel mounted on the closest side in the photo!