Well, I gave it another shot, and the best I could measure the very last gear (38 teeth, with the extended plastic) is 2.25 module, 20 degrees pressure angle (nearly perfect match). The 12 tooth gear, the one I was interested in, does not appear to be the same, by a good margin, which is obviously very weird.
Since I'm not a gear expert, not even a mechanical guy, I'll leave this one for the MEs out there. For our application, close enough was more than we needed, so we just drew the gear profile "by eye", machined it on our home-made CNC mill, measured, and iterated - only took two shots!
