I’ve never done anything close to the color calibration work, in part because my vision is color-deficient by default, so any tools or processes relying on my own visual acuity isn’t going to come out right.
However, I was under the impression that there existed external tools that basically did exactly what you were trying: Taking actual images of the screen in a controlled way and comparing it to physical (or at least a known-good digital) copy of that same image and outputting the “right” profile.
Is that made-up bullshit someone fed me and I never cared to verify it?