I'm machining sheets of thin 1/16" ABS sheet to affix to later affix to wood parts. My experience today was in making some rectangular, long strips. As I machine the first three edges, vibration can start to become an issue, but as I machine the final edge, the part starts to lift, vibrate, and interfere with the cut.

Tabs seem to be a potential solution, but leave a bad edge, and are a lot more finicky with plastics. Are there any other machining strategies that can prevent these small parts vibrating, and coming loose?