This is so cool to receive a response from the creator of Hexapipes! Thank you for the reply!
That makes sense re: the Penrose grid being different and not having enough data in the numbers to make sense of yet.
Based on your help, I've decided to start with the square grid, and I've gotten as far as a simple program that can take the JSON and render a puzzle as a png image. Now to draw the rest of the owl...