If you can get the spindle out with the stuck arbor, I would do that. Beating on the spindle bearings can destroy them. A TAP is fine, But beating hard enough to mar things can also damage the bearings. Ball and/or roller bearings really do NOT like impact loads at all.
Once you get the spindle out, there are a lot of ways to attack getting the arbor out of the spindle without doing further damage.
Look at how nice and tight a MT holds a drill in the drill press or the chuck in a tail stock by just popping it in with hand pressure. Think how tight it must be if you are agressivly cranking down on a draw bar. My guess is that you are going way to tight on the draw bar.