so I assume you want to keep the frame sized middle part?
one easy hack would be to make a circle outside of the part you want to keep, but just about not touching it… right at the spot where the bit will enter for the “real” cut.
If you cut that one first (and make it say 2x the diameter of the bit) with a pocket, by the time the real toolpath starts, it can enter the wood without any force on it since you already removed most of the material in that spot.