Revisiting a Quaternion Rotation Problem

I must apologize, I think I neglected to explain what might be an important detail: My GameManager is situated in the very center of my cube, and my camera is a child object of the GameManager and is positioned such that it is held away from the cube and “looking” at the cube. My rotations are achieved not by rotating the cube, or the camera: my rotations are achieved by rotating the GameManager in the center of the cube, effectively moving the camera around the exterior of the stationary cube, making it appear as if the cube is rotating when it is the camera revolving around the cube like the moon revolves around the earth.

So when I tried

"desiredRotation = transform.rotation * Quaternion.AngleAxis(degrees, axis);

My Y-axis rotations still work fine, but my z-axis rotations just wobble in a circular motion:

https://www.youtube.com/watch?v=x0kA1xEJXRg

Thank you sincerely, and I hope I haven’t wasted your time.