Long ago we used brass bars with a ball end in a tool post mount to true up work in an engine lathe quickly. this would get you within about .002-.004" runout on the OD very quickly in a 3 jaw, and could get you about.002 runout on the face in either a 3 or 4 jaw. This is a modern version of the brass nub. Uses a Bearing instead to rotate with the work. now using this tool, I can true up work to within .001" or less, OD or face, within about 3 seconds. If you make one remember to run it on center line with the work, and at a low rpm or you will burnish it.
P.S... I know the surfaces look horrible... just never got around to grinding it or polishing it... someday I suppose.