Really useful details, thanks Bert.

When you see the error from moving along the projected line, is it random noise or is it like the line is bent up or down in the middle, like your gantry measurement ?

I think I have seen the line bent like this. I did a little experiment with a dot laser and a glass cylinder (wine glass stem). When the laser passes through the cylinder at 90 degrees you get a straight line projected, when you angle the glass a lot you get a visibly bent line either up or down depending which way to hold the angle.

Maybe this is a common problem with the line optics, and maybe we could calibrate it out by taking two sets of measurements along a straight edge with the laser flipped 180 axially for each set. Will have to think on this, any thoughts welcome...

Although it would not be easy to flip your laser as it is on a pendulum.