From the looks of it, your plywood is roughly level with the highest point on the monitor.
If so, I would get a large piece of paper that is thin enough to see through when backlit, turn the monitor on, mark the paper where the edges of the screen are, and then cut a piece of black posterboard just outside that area.
That would let you just lay the posterboard over the plywood, and cover everything except the usable area of the monitor.
If you use smoked plexi over it, you shouldn't even see the edge of the posterboard.