Routing Gears for Gear Toy

I've been working on a gear toy project for my granddaughter, for over a month now. I have a full set of gears cut using a bandsaw, belt sander and scroll saw sanding blades, from medium density fiberboard (MDF) (see photos below). But, even though I have been very careful to sand "to" the lines, the gears don't mesh right. I've even sanded the lines away and they still don't mesh right. (Last photo should be first, showing bandsawing the gear. Second photo shows how the bottom of one tooth was cleaned up and squared off using the bandsaw and the following photos of the completed gears.)

The gears mount on peg board and I found it difficult to figure out how to locate/position the gears at first. I figured out a handy way that I think young kids like my granddaughter can work with (they may be able to do it better than this old f*** anyway) that I may comment on later. The problem I'm having with the gears is that they should mount directly in line in the 1" peg board hole centers (I think). But they are too tight that way. So, by shifting over one hole, I can get the gears to not bind, but then there is more "clearance" than there should be - again, I think. I've set up full gear trains this way, but it is just not satisfying for me. Gear Train in Motion You may notice that few of those gears are mounted with their centerlines "inline".

Plans for the gear toy are out of Wood Magazine and are available for purchase for $7.95.

I want to remake the gears from Baltic birch plywood (BBP), but want to get the gears meshing right before investing anything more in time and materials, etc. To that end, I found a gear program that allows for creating and customizing gears for this sort of thing. Woodworking for engineers
There are also quite a few plans for gear toys/machines available from this site.

I've designed the exact same gears in that program with 1/32" "slop" and they look like they should work. I've imported the gears designed with that 1/32" slop into my CAD program and have worked up "patterns" for printing and mounting up for hand-cutting in the manner described above. I want to cut some trial gears, but it is almost no extra work to cut a stack of three or four, so then I get sucked into remaking multiples, and then into remaking all of them.

That is when CNC comes to mind. I mentioned this in another thread and David (difalkner) PM'd me about that, mentioning a thread he posted about making some gears using CNC.
https://www.routerforums.com/show-n-tell/136765-enigma-cipher-gears.html

I am now interested in learning more. The balance bike project that I posted about would have also benefitted from CNC, rather than the pattern boards that I used. But I was no where near interested enough then.

Rick