OK, tried in any possible way with parenting, it doesn't work.
When Unity imports a model with Z up, it flips it 90 degrees on X axis.
If you add a dummy to correct this, for some reason the MouseLook action still finds the first parent object and refer to that as "world" axis.
I attached the orbit system, have a look if you have time.
First use it as it is, in the world. It works.
Then make it a child of any imported object from a program that uses Z up, and you'll see.