Man, I thought that would totally work. It's a great idea but it seems that wont work with a action using Forwards (like QuaternionLookRotation or SmoothLookAtDirection).
I can swap and invert the values and have it change it's behaviour but it doesn't seem to change the fact that it's using Forwards.
It's not easy to see but even swapping the Y and Z values, the blue forward vector is still the one mirroring the circular motion of the Up green vector on the right box.