The solution is so obvious it completely escaped me 'til now

Well, it almost works. Here is the default appearance after clicking apply in the custom column dialog. Notice I put an empty column directly after TC's internal extension column so that the icons don't overlap the values in the new extension column. Also disabled folder brackets.
Example 1
Another appoach that works is to just widen the new extension column and right-align it, instead of adding the empty column.
You can drag the vestiges of the original filename and extension columns to the left to hide the headers, but unfortunately TC won't remember those widths for very long:
Example 2
Here are my requests:
Please enable users to...
1. Set (and maintain) Filename and Extension widths of 0
2. Disable "ellipses" in the filename/extension columns (if desired)
That would make my display look like this (ie, PERFECT!):
Example 3