This is how I work it out:
200 steps / shaft revolution * 8 microsteps / step * 1 shaft revolution / 20 teeth * 60 teeth / arm shaft rotation * 1 arm shaft rotation / 6 “units” = 800 microsteps / 1 “unit”.
So 800 looks right to me. I computed 533 for my imaginary machine, but that assumes 1/16 microsteps and not using a 3:1 ratio.
I don’t see a reason your X and Y should be different.
Does the X axis affect the Y shaft? It seems like it would if that gear if firmly attached to the X shaft.