Here's another thought - not a machining strategy+ though!

When we do small parts like this, we sometimes use double sticky carpet tape to hold them down. Clean the surface, tape down, place the part. It has been very effective for us, and cleanup is easy (acetone or laquar thinner do a nice job). It will hold the pieces in the center as cut outs and keep them from getting sucked in to the cutter.

Another tack is to use supper glue - however, it is harder to clean up. We use it a lot for fixturing. If you can heat the parts to 400°, they come off easily as that breaks the bond.