Here at work I do not have TG, so just to let you know that I can't check your file and will only respond to your initial finding and question and share some thoughts with you, no solutions.
If you have a line on the Z-axis then warping it along the same axis would only move the line along that axis without perturbing it sideways.
So to me it makes sense that when you rotate the warp function 90 degrees that the effect is different.
Perhaps I should check the file, but just reading this initial observation rises questions on my side.
The other aspect to warping is noise-shape of the warper. For example:
Create a ditch on the Z-axis in the terrain using a simple shape, as if a base for a canyon.
Compute terrain.
Displace side of canyon laterally on X using either billow or ridge noise, does not matter which.
Observe the difference between the left and right canyon.
One side will be billows and the other ridged. Swapping noise type will only swap right and left.
Thus one side receives the positive displacement, so to say, and the other side the negative/inverted.
Perhaps this contributes to the things you see.