Here are some tips for making items like these, this set is Pokemon 52 through to 102. I cut the 9mm ply on a fairly high power, this ensures that the cut goes all the way through regardless of blemishes in the material and then you know each piece can be easily removed. This causes quite a lot of burning on the underside of the material due to reflections from the honeycomb bed. Once a set has been cut I often secure all the pieces back into the framework using masking tape across the top side of the material. This allows me to lift all the pieces out of the machine at once. I can then flip the whole sheet and sand the reverse down while they are still in the framework. It's much easier than juggling individual tiny pieces.
I guess for something like this you could also mask the reverse so that most of the burning would be on the masking tape instead of the work piece.