For squaring, I had good results with the 'five cut table-saw sled test'
https://www.youtube.com/watch?v=RZ_nzvYEZ-4,
https://www.youtube.com/watch?v=oCwQn40GsVs
For my tests, I made a fence along the Y axis to rest the stock against (mimicking the sled backstop), then run the spindle from X0-Xmax down the edge of a square piece of stock. Rotate down each edge, then the last pass you cut a wedge instead of trim. Measure the difference between the two ends and that's 4x the error.
Thanks for the notes, I'm also working through the same spindle upgrade this winter.