Two stacked plates with the display would be about 41mm which will easily fit inside the enclosure. If you turn the Pi 90 degrees from what is shown in the photo, you could even mount 2 side-by-side. Mounting might take a bit of ingenuity. The board-edge connectors would work, but you might need slightly longer screws: http://www.adafruit.com/products/1116
Another option would be to mount the Pi to apiece of 1/8" material with the edge mount kit, then screw the whole assembly down to the mounting bosses on the bottom of the box.