When stack cutting, I use either 5 1/8" material or 3 1/4" material. If the pattern is fairly simple, I fasten the stack with either 5/8 or 3/4" brads in the waste area then cover the stack with blue painters tape to which the pattern is glued then covered with clear packing tape. This makes for easy removal of the pattern when finished. For more complex patterns, the stack is held together with the blue painters tape then finished as before. I sand the finished project by laying it flat on a solid surface and sand with a palm sander making sure to hold the sander square to the project. I have had good luck with this method without breaking the project.
It is also important that your table be square to the blade. I keep a 6" level nearby to periodically check that the table is level from left to right. If your cut pieces will not slip out top or bottom, it means your table is not square.