Roger,
(RTA = Radius Turning Attachment)
I start by locating the center of the sphere (the pivot point of the RTA), by finding the OD and end point of the stock. Somewhere within of those two points lies your sphere center and RTA pivot point.
Once your RTA pivot position is set, and some rough metal removal is done to get to a ball shape, the cross slide and carriage shouldn't have to be moved as neither have an effect on the radius of the sphere, only on the location of the RTA pivot point.
If you are doing a hemisphere, and the finished radius is set, the carriage advance toward the headstock could be used to get to fresh metal and a finished surface, but once you pivot the RTA beyond 90° (ie, beyond turning a hemisphere) any carriage advance would ruin the sphere.
My RAT (home-built) has a threaded advance (in-feed) and the final few finishing passes are done with that.
I'm not sure if this helps but I hope so.
And yes, from time to time chuck clearance can be a problem.