Am I the only guy here that sees this as a simple one and done job, on a faceplate? Could do in a four jaw chuck with the jaws outboard, but that has the non-benefit of potentially warping the face of the disk as the jaws are tweaked tighter.
The object IS to get the face of the disk to run true, no?
Seems to me that the simplest answer, is to put the face of the sanding disk against the known true face of the face plate (it had better be true, or it's not much use as a faceplate!).
Bore out the hole to an appropriate sized piece of round bar, set that in place as you see fit, I would suggest a permanent bearing retainer Locktite type product. Drill and bore to size for the drive shaft. If you REALLY doubt your abilities to bond the bushing in, you can afterwards drill and tap a few setscrew holes along the joint line between the two parts, use the same bonder for securing them permanently in place. You will need a thicker wall bushing, aka: larger diameter stock, and hole for it.
I don't see any advantage, and lots of disadvantages, to gripping on the pulley. Main one is that the pulley is die cast zinc crapola, and while easily replaceable, those type are not well known for their nearness to perfection...