As mentioned by SCh5 about the gap not being perfectly parallel the the plane of the handle, the camera has a slight tilt. I know you are going to try to get some better pictures to work with, so don't take this wrong, you are working with what you have. I grabbed an angle finder and a razor and estimated an approximate tilt of 3 degrees. To visualize what that can do, think about photographing buildings. There is probably too much going on to make guesses about this image, but I would believe the differences you are getting are a compound effect of several distortions. I could probably derail this into a discussion about field curvature of optics, but that's enough for now. I have ideas about how to make a DIY comparator.Lol. Don't be sorry, you were actually right. Blade exposure is measured perpendicular to the shave plane, which is not what I was doing.
The corrected blade exposure measurement I get is .157mm, which is bigger than the .13mm stated by the manufacturer, but I'm pretty happy with being within a few hundredths of a mm. The gap is only off by a few hundredths of mm too, which I'm pretty happy with. It looks like a reasonably accurate way to get measurements with $40 worth of equipment. Once you have the picture, it's about 5 minutes worth of work to get measurements.
I think ImageJ will probably do a better job than my proof-of-concept attempt with Powerpoint, especially if "focus stacking" can make the reference lines a bit crisper. Here are the updated measurements:
TLDR: you did a good job with what you have.