DNice
I had another look at the profile you sent, really due to the new LUT Size capabilities we are adding to ColourSpace.

And this is the Red response.
So I suspect the Magenta and Yellow issues are propagating from the Red.

However, I have had a thought based on the regularity of the step-change error.
I do not think this is actually a displays issue in the sense of something that can be calibrated out.
I think it is a D-to-A or A-to-D error, either in the display or the probe.
If that is what it is, no calibration will rectify it, as all calibration will do is move the point at which the D-to-A or A-to-D error occurs, based on the remapping of the LUT.
And in reality, the LUT would appear make the issue worse, as it would be trying to correct an un-correctable error, introducing more errors as a result.

All the points raised about the non-monotonic readings, as well as the LUT Granularity remain.
(The fact ColourSpace can now do 256^3 and great LUTs means nothing for the display, as it is locked to a 33^3 LUT.)
But I do now think the issue in in the D-to-A or A-to-D.

Steve

Red Error