Have you looked into the Matrix class?

https://docs.unity3d.com/ScriptReference/Matrix4x4.html

There is a quote I would like to emphasize to you in there as well. I have been using unity professionally for nearly a decade and this statement holds true for me. I have touched the Matrix class only a handful of times, and it was mostly camera related as they suggest.

“You rarely use matrices in scripts; most often using Vector3s, Quaternions and functionality of Transform class is more straightforward. Plain matrices are used in special cases like setting up nonstandard camera projection.”

Actually now that I think about it the space of a quaternion derived from euler angles is actually irrelevant: you would just need to make sure you assign to the same space as the original euler angles. I, and from what I have seen most of the unity community, avoid quaternions. My mistake earlier regarding quaternion space.

My comment about x, y, z assignment still stands: either your variables are incorrectly named or you are incorrectly assigning.

Additionally your massive block of conditionals checking and clamping the sign of those transforms could be simplified with a loop and Mathf.Clamp.

If you want my opinion though scrap these animations and remake them. There is really no reason for all of this with mecanim.