I think that all these mount-dependent details would go away if the centering routine followed the method I describe above - which I have confirmed works to the arc-second level with my mount. Just follow the routine and allow an option to sync the mount once centering has completed.
The issue of syncing the mount to make the plate solve work better is somewhat chicken and egg. SGP can only sync the mount after a successful plate solve in the first place - so if it fails nothing will happen. I suppose you might want an option to sync at the start of the centering routine rather than at the end - or in addition to the end. That would make the plate solves happen with more confidence.
But my main point is that if a mount misses by a very consistent amount during centering - as many do for many reasons - they would most likely center very well with the method I have described - with an option to sync the mount or not and the beginning and/or end.
Frank