Very nice implementation with the 3d printed gears. When you get down to cutting gears from polycarbonate, you'll need to take some precautions. When cutting small gears like that, you'll need to pay attention to the laser kerf and account for it in your gear design. You may also need to cut thin slices and stack them depending on the focal length of the laser lens. (A short focal length lens makes a shorter, more angled cone, leading to either an angled cut or a larger kerf in the material.) Stacking multiple thin cuts helps alleviate kerf and angle issues.
Also, polycarbonate cutting fumes are toxic. But you can't leave the laser fully unattended while cutting, since flame-ups and fires are possible in the laser cabinet. So be very careful, or get help from someone who has done this before.
To account for the kerf, you have to either scale the drawings by the kerf width or design with the kerf width in mind. Which means you need to know what the kerf width is. It will vary from laser to laser, and change with how dirty the optics are and how well-focused the beam remains.
To accurately measure the kerf, cut multiple identical rectangles of known size from the material you will be using, then lay them long-edge to long-edge on a flat plate. Measure the total distance across the rectangles with a caliper. The kerf is then:
((n * design width) - total measured width)/(2 * n)
Where n is the number of rectangles. A good number for n is 8 or 10, but don't use fewer than 5.
I can help generate the gears in .svg format if you need that, but since you've already been able to print them, you may not need it.