Skew correction/perpendicularity correction (millkins or millkins_xyz)

you need to install the build dependencies. See 4.2.2 in the linked documentation above.

1. Note that the compiled installation is separate from the package installation you worked with before so you need to modify '~/linuxcnc-source-dir/src/emc/kinematics/trtfuncs.c'

2. then cd to ~/linuxcnc-source-dir/src and run
3. if that was successful you can start the compiled installation:

That is correct there is no skew correction in identity kinematics. Note though that my modifications are NOT what you need as the skew is in the work coordinate system (ie the correction rotates with the table) which is not correct, you want the skew correction to be applied to the machine coordinate system (ie it remains oriented to the machine joints regardless of table rotation).
To make a serious effort to get this working I would not bother with the built in trt kinematics but would use the more recently added userkins.comp template and build a new kinematic from scratch.
Re userkins.comp:
forum.linuxcnc.org/10-advanced-configura...mill?start=30#258311
For an example of how to derive a kinematic see:
forum.linuxcnc.org/10-advanced-configura...mill?start=80#263694
The finished kinematic see:
github.com/LinuxCNC/linuxcnc/blob/master.../xyzab_tdr_kins.comp

To derive the forward and inverse kinematic model I would recommend using jupyter notebook and ipython. However, you need to be, or be prepared to make yourself, comfortable using matrices.

For an easier start on how to use jupyter notebook and ipython to derive the kinematic linked above you can directly load the notebook used to create it and the documentation to study/modify:
github.com/Sigma1912/LinuxCNC_Demo_Confi...0Kinematics%20.ipynb
This contains all the python code blocks that handle the math.

So my approach (which may be wrong though) would be to start end the kinematic chain with a matrix for the skew (also called 'shear') which has the form:
 

The inverse looks the same with the shear elements (ie lambda and mu) negative