Success!
For the top bearing, I used 6 shims instead of 3.
For the lower bearing I use 5 shims instead of 4.
The spindle shaft has a very very small amount of vertical play when outside the quill assembly. I figure HEAT/expansion will cause it tighten on itself from within and so I did not tighten the upper bearing dust cover cap any further.
when placed back into the milling head, the vertical play is all gone.
I probably didn't need the 5th shim on the lower bearing, but wasn't going to press everything apart. The lower bearing dust cover is flush with the spindle housing.