Love the story! At one point, you are asking about the purpose of the giant hole in the backside of the display: The most plausible explanation is that, it is to allow air circulation within the device to prevent overheating.
Another explanation that I saw [0] was that it was for people to pop the back panel out. I think this is the most likely explanation but it didn't occur to me while working with the sign. I feel like a little notch would have been more appropriate for an actual product.
That particle board material would crumble too much if they used a notch for removing the back. I've seen other items in similar cases with the exact same drilled hole in the back cover. Many used staples to hold the back cover on as wood screws tend to damage the (other) particle board used to make the sides. The "designers" probably used it because they had some other item at home (stereo, TV, loudspeakers or clock-radio).