I use the same surface for drawing that I do for carving, and I can’t really put a hole through it, so here is my bench dog solution. I opted for holes at the edge where they won’t interfere with the drawing surface. For now, at least, since I don’t think I have to use much force when clearing large areas of waste, this will work.
Here’s the outside kento I built for the heron print. The blocks vary in thickness, so I have to prop some of them up. I used a chunk of yellow pine to make the registration block on the bottom, and boy is it hard!