center point change after rotating XXT

[[Pa...]]

I have a machine that is failing a positional ring gauge test. The gauge stands upright on the granite with the cylinder aligned +Y / -Y. I measure the gauge as a cylinder with XXT head (5x50mm probe) rotated to +Y.
The software is aligned:
1) Level to face of ring gauge
2) No rotational reference
3) X and Z origin to center of cylinder
4) Y origin to face of ring gauge.
I then reverse the direction of the probe 180d to face -Y and do not change the alignment. I remeasure the same points on the cylinder. The diameter and form of the cylinder are within expected tolerances, but the X and Z positions change by up to .001”. Notes:
1) Using a cylinder vs a circle as the origin is problematic due to projection error. I’m doing it this way as it most closely resembles the real world program. I could use a circle or create the pierce point of the cylinder axis with the face of the gauge and use that as my X-Z origin, but I don’t think this is the source of the error considering the quality of the gauge.
2) I've heard the comment that XXT was designed for maximum flexibility, not maximum accuracy, and that I should consider XT/rotary table for this part. Any opinions on this?
3) Should I consider changing out the A-B rotating mechanisms? I know they are easily damaged.
Thank you.

[[No...]]

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That should already happen when the base alignment is being calculated. Unlike other measurements, Caylpso uses the intersection points of elements for the base alignment.

[[Pa...]]

and what is your best thinking as to what the problem is then?