@Boomer, start with an alignment jig (mentioned by @fred_dot_u). The first step in good centering on the object in the chuck is a well centered rotary. A jig will ensure that every time you place the rotary on your bed, it is in the same spot consistently. This works well with having a saved position in the move panel:
Before going into more detail, am I on track with what you’re asking, or were you asking about suggestions on methods to chuck the object centered in a manner that it rotates without wobble?