The three jaw sounds like over kill....... A set of bearing mandrels could be in order....but a crap shoot there also to get the exact size you need! IF you have a metal lathe you could cut one to size or simply make one....... Goose tool #241......
Either a finer tipped punch (gently grind your old buggered up punch flat (if not already!) on a fine grinding wheel!)...go easy on it tapping it out..... OR just haul your two hubs down to a machine shop and see if they have a set of mandrels that will fit inside the hub directly on the small race sticking out....and they can then press them out.
It's always something......!
Steve