First let me say that what you find by machining a piece of wood and measuring is just not the way I test.
Using measurements just eliminates any thing to do with possible code or actual cutting.
Simply put, steps / unit from pc = a linear distance of travel movement.
You calibrate the axis for only one section, say the left, and then test / check what the error is across the joint and also the right section.
Now you know comparative error amounts. For the joint, you position to the left of the joint by approx 180 degrees of the pinion travel, and then move another 180 deg of pinion travel, which puts you on the right side rack.
SO,
You can compare the two different racks separately for linearity of movement and after that you can check across the joint.
How would I do it with my equipment?
I place a 48" calibrated scale, which is accurate to within 0.001" at each 0.1" division and can measure to within .0002" in between the divisions.
An optical alignment scope with measuring capability ( optical micrometer ),is used to read the scale.
The axis is moved and readings of movement are taken and the linearity is plotted. I have even checked the reverse movement as sometimes the reverse movement is
different than the forward movement. So one easily and quickly profile the movement.
One can accomplish the same thing with long calipers or a known reference but it is cumbersome to do for long distances.
BTW,
If one has a nice 48" Starrett scale graduated in 0.010" and calibrated you can use that along with a cross haired optical magnifier.
Also make note of what Jerry said as the pinion contact on the rack may be different along the rack and would affect travel.
RICH