One thing to keep in mind is the axis you use for rotation. “Rotating a plane” only works as expected (i.e.(without tilting it) when the rotation axis is perpendicular to the plane. AS far as I know, that’s not guaranteed in any of the colour models used, nor is it clear how the “hue plane” is cut/projected.
So, unless you are sure that your model is what you want:
- i.e. a polar representation
- with hue as the rotation,
- one of the remaining two axes in the plane, and
- the third perpendicular to the plane,
you’ll get unexpected effects rotating your colour wheel, as you will also change the two other values (and not just the hue) for each point. And as important, even if you create your colour wheel correctly in one colour system, it doesn’t have to be correct (for this use) in a different system (as systems differ in how they define their basic axes, in lenght and in orientation relative to other systems)
I don’t see a clear specification of what system is used to create the colour wheel, nor in what model it is rotated.