David- .001 on removal/replacement (repeatability) is pretty good and you're not going to get better than that without exponentially difficult changes.

Nice pix- I now see how you've set it up. If it works OK you've lucked out but I really think you might wish to calibrate it or check its inherent accuracy with a tube of known wall thickness/uniformity.

I suspect the deformation of the lower bar is negated by the barrels - sort of a compensatory mechanism. Ordinarily a steel bar sags appreciably over that length.