Here is what the masks ended up looking like when they came out of the laser cutter!
Because we couldn't find wood that was both thick enough and wide enough to fit all the masks into, we ended up adapting our method of fitting them together. We laser cut little joints that connected each side of the mask. Once the joints were in place, we traced the position of the masks on our remaining piece of wood (our base), uploaded a photo of the traced wood to Illustrator and traced again within the program. This way we were able to laser cut the small slots for our masks. Here's the final product! It's not really a "box" so much as a ceremonial candle holder, but we're still pleased with the result.