This was the end result of centering all of the circles of the collimation
laser. While the central shadow is now centered within the bright rings, you
can also see that at the bottom of the set of bright rings, the beginning of
the next ring is just becoming visible, and yet this edge of a ring does not
extend all the way around. Further, while the dim outer ring is better centered
(though now I can tell what I could not tell at the time, that the inside edge
is still not quite centered vertically around the brighter rings), the width of
the dim ring is obviously not consistent.
This led to a test of star images with CCDInspector
(see next image).