Scott,
A previous place I worked for did die-cutting. We used an ancient Heidelberg machine, also used for numbering and perforating. We also had a hydraulic press, similar to the machines used for making number-plates. (just bigger, bed size appx 600 x 600mm) The dies we had made up at a litho printing company, they made them with the blade cast in lead. I’m sure you could use more modern, more flexable technology like a CNC router (with blade i.s.o. spindle motor) or lazer engraver to cut your substrates. Take a sample to a local signwriter with lazer engraver, and ask him to cut whatever design from it. If it works, buy one, and do it yourself!