That does look pretty complex, and your ideas are sound.
If you haven’t been selected for the Passthrough Beta project (which closed to volunteers a couple of weeks ago) then your method should work out pretty well, although it’s going to be very difficult to match across that many cuts in the design perfectly. Make sure you are anchoring the material against the side of the tray to keep it from rotating when you slide it.
Matter of fact…there’s a tutorial on doing it in Illustrator here…be sure to follow the notes at the bottom closely, they help the most.