... Besides if you are doing really close tolerance work you will want to true your chuck jaws occasionally anyway and that does exactly what you are talking about.
This was my next thought as a way around having to "rebuild" the spindle. Could you make a set of soft jaws for the chuck and machine them to take up the runnout? Not the most ideal situation, but i don't know how much you want to spend. Sometimes the best "free" things cost us much more.