Hi,
but also because I am curious and I like the challenge of figuring it out. Does that make sense?
Yes, it does make sense. Remember I've done both of these things, namely attempted to get perfect spindle speed, and have also 'perfected' rigid tapping with a C axis spindle....so yes I understand the challenge....
its just that there are more important things you could do with that effort and resource.

ATC, flood cooling and filtration, chip conveyor, through-spindle coolant, shrink fit tooling, four and five axis tool center point control....and the list goes on.

want to figure out Servo tuning using an oscilloscope,
Why? You should be using AC servos. I use 750W Delta B2 servos and they have free tuning and set-up software. Included in that software is a 'software oscilloscope' especially tailored
for tuning the servo. It can display things like 'following error', servo current, commanded input and much more besides. Then you can tweak the tuning parameters (PID) and watch
the response live and realtime!! right on your PC. Not that you really need it, these servos have a software Auto-tune feature which make manually tuning servos nearly pointless.

I use Delta, a Taiwanese brand made in China, but also DMM, a Canadian brand made in China, are both good quality, support, documentation and most importantly set-up software at fair
prices. There are a whole swath of cheap Chinese servos, and to be fair to them they do work and are attractively priced, but the documentation is poor to shocking and often no set-up and tuning
software. Many people buy them on the basis of price without ever considering how they will set up and tune them. That is a mistake. Pay a bit extra and get Delta or DMM.
There are of course better servos again, like Yaskawa, Fanuc and Siemens....but if you have the money for those...then why build your own machine?

These old school DC servos (that require you manually twiddle P,I,D knobs) are for the birds. Get up to date.

Craig