The error of the chuck mounting on the backplate itself should be zero runout (ya Ken, so I'm fussy ). The backplate should have been machined to exactly fit the recess in the back of the chuck, such that no amount of tapping with a hammer would ever move the chuck at all! That's how us professionals do it
After you've got more experience under your belt, you might redo the chuck mount some day. Just mount the backplate on the thoroughly cleaned spindle and machine it right on the machine it will be used on. You might have to face off the existing boss if its too small, or de-centered. There's usually ample thickness to the backplate casting so you can take a couple of stabs at it.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)