Just yesterday I approved a PPAP for a high volume part with a Cpk > 5 on a 0.008 mm wide tolerance band. Admittedly that's the highest Cpk I've actually seen in the wild, but if you understand the significance of that you'll also understand that it requires excellent process control, and a very consistent measurement system, to achieve.
1. While I did throw some snark in there, basic calibration should always be done if you're to the point of an R&R.
2. Throwing in some more snark, a gage R is probably more relevant than an R&R unless you expect the OP to conscript 2 friends for this study.
3. My main point was more about appropriate levels of effort for the task at hand. The OP has already concluded that his measurement technique needs improvement. An inspection of the measurement system is a lot of work to confirm what has already been concluded. A lot of time some common sense will tell you if your measurement system is sufficient without the rigor of a full study. Other than the gage R&R part, the rest of the post seems to be good relevant advice.
4. Assuming that a lower force indicator is not available, stiffening the system up and measuring closer to the attachment points would help. At first glance the setup through the rear dropout looks stiffer than the plate attached to the derailer. I'd set the indicator up to measure directly off of the inner cage plate at the pivot.
5. Sprocket spacing is probably a published value, and can be easily determined by measuring a cassette off the bike. Ideal lateral derailer movement should match this value, so we know the target as well.
Knowing cable pull and knowing derailer movement aren't quite the same. I'd expect the derailer to have equal movement per shift from one end of the range to the other. I would expect cable movement per shift to vary slightly to account for the change derailer geometry through the range.
I'd measure cable pull as close as possible to the shifter. Taking it right at the downtube is a good start. When I did it I clamped the handlebars to a bench (granite surface plate in my case), put a pulley and weight on the cable end, and measured travel right near the cable. This removes the housing, and associated error, from the system.