Hi Chriswhill,
I have not seen you set up, but Hair is not bind at all in that way. Hair is connected to the polygon directly. The bind uses polygons, which becomes “connected” (bind) and weighted. Your hair would be have the need to be based on polygons to do that. Typically it is not, it is as default a Post Effect.
To my knowledge—there is no direct way to bind with weighting Primitives. Are these eyeballs based on “Sphere-Objects”? (Direct vs Mesh-Deformer)
The eyes, I guess there are more opinions about, should not be bind—they should move completely with the joint data: such as in hierarchy or “Constrain Tag”. I don’t think the eyes need to be deformed, they should just move. Again, there are perhaps different ideas about.
If you can provide a reduced set up, not your whole character” then I will look at it.
If you think that is a problem caused by C4D, then please contact the support.
All the best
Sassi