Wrong, the values are defined by ISO 12641-1997 standard,
The paper you cite does not say the values are defined in a CIE space. Even if they were, it's absurd, because as anyone who has actually ever looked at targets conforming to IT8.7/2, they are not even remotely the same amongst each other. The paper you cite rather clearly demonstrates this fact.
Or you can buy whole standard if you want. Values are not in LAB format but you convert it to LAB without problems.
OK well if you consider the choice of reference not a problem. I'd consider it a rather significant problem if your goal is to avoid arbitrary decisions and results. You do not have a single reference available here. Period. You have nothing like a TR006 (which correlates CMYK to LAB) that's agreed upon by your industry, nor the equally important issue of tolerances. You can't have the same tolerance for all colors, you realize why don't you?
You can do this with IT8.7-2 too printing the target is far cheaper than buying the colorchecker SG, in fact there are numerous sources for IT8 targets that for reasonable prices.
YOu're not buying an IT8.7/2 either. You're printing it. So why print that target as your control slug to verify the correct output of an "RGB" output device, rather than either the values in the original Color Checker, or Color Checker SG, or some other target?
Colorchecker SG does not have 22 grayscale paches to begin with, it also lacks the CMYK RGB step values available in IT8.
Have you ever seen press process control use 22 grayscale patches? Have you ever seen it use more than 4? Why do you want more? I can imagine some good reasons why, but unless you're really clear about why, you're not really going anywhere.
The fact of the matter is, your industry doesn't have standardized print behaviors like the print industry does. So anything you come up with is somewhere between arbitrary and subjective.