I didn't take any photos but used the same air die grinder in a photo on the other thread, (use the link I posted). I stone is about 1" diameter, 60 grit if I remember. What I did different this time was to clamp the die grinder to the side of a 4 way tool post instead of the Rube Goldberg I used the last time. That was a shorter, more solid set up with less (no?)flex. I spent a lot of time matching the heights of the jaws on the deep end and a lot of time making sure the slug was square in the chuck prior to grinding. I also set up a stop to keep the grinder from crashing into the slug. Many light cut passes with the stone, and even lighter near the end until almost no sparks.
Have you checked the chuck over a range of sizes? You can usually expect the run out to vary as you do---so if yours doesn't, you have a scroll that is well centered and very round.
I ground the chuck with a slug approximately 1.5" and checked with a short length of round stock about the same size but turned round. There it is .001" run out. From there I went to some 5/8" cold rolled for a project and it was .002". All new metal stock is suspect to me, and sometimes I can visually see improvements by rotating and trying different positions in the chuck.
It's still a three jaw and I will treat it as such, too many reasons for them not be perfect (if there is such a thing) but somewhere under .003" is something i can work with. The old chuck was loping like a camshaft at around .010" TIR.
Regrinding sure beats a few hundred for a new chuck and all the work to set it up. I noticed new chucks are advertised with various degrees of run out, less run out = more $.