Scrollsaw Tip - Stack Cutting
Try using double sticky tape to stack cut your parts. Buy the kind in the painting sections or the building supply stores. It comes in 2" wide rolls. It holds well enough to run parts through a router.
To seperate the parts, use a 2 1/4" blade in a #2 X-acto handle. This will allow you to cut the parts apart without denting the edges of the wood.