...for this particular job you need a bottoming tap, which is a little more exotic. And it needs to match up with anything you can cobble together as your puller. But yeah, nothing makes me happier than inventing a way to do something on a bike repair that seems impossible and requires some head scratching.

For instance: if the arm you can't pull is the non drive side, you can pull the drive arm, and with a loose ball BB you can usually slide out the remaining non drive arm, adjustable cup, and the spindle. Then you take it over to a decent bench vise and carefully pound out the spindle with love and hammer, using the vise (and maybe some wood blocking) for support.