Intricadoodle - Puzzle

For 11 years I've been wanting to turn my 'intricadoodle' style of characters into a puzzle. At the time, I couldn't wrap my head around the production process. But now with having access to a laser, I gave it a shot as a gift for JibJab's CEO, Gregg Spiredellis.

 

Original sketch:

Making it vector in Illustrator: 

Under the laser:

Mounting the back: