The track and backplate needed to be cut out of acrylic.
This was difficult because the nature of the wood causes it to warp a bit after cutting. I let the wood sit for 3 days, then scanned the piece on front and back to custom fit the opening and the backplate. I had to be sure that the plastic fit snug with the wood but also that the track be a perfect circle for the motor mounted at a central point.
I then traced the scan in illustrator and cut a test out of paper before taking it to AMS to have it cut. This method worked nicely and was way more accurate than measuring any other way.