Quite interesting!
I notice the original board has strips of wood on the ends, running perpendicular to the grain of the main part of the board. I've seen the same feature on old wooden drawing boards. Perhaps those strips serve to prevent warping.
In woodworking that is known as a breadboard edge. It's a rather common way of finishing the end of a large surface. Yes, the purpose is to prevent, or at least limit, warping.
If you are still looking to produce paper hold-down devices, I suggest you look at 3d printing using a hard plastic. Once you have a design file, multiple parts would be cheap to make. I've seen my sons make close tolerant parts such as hinges. I'm thinking an table insert with female threads and a compatible screw down part with a wide top to hold the paper.