If you can't get enough purchase on the pulley to lock the spindle, try another way to clamp the spindle such as mole grips. Without protection they will damage the spindle so wrap it with a piece of leather or something similar. It might also be worth trying to attach a lever to the faceplate so once you have clamped the spindle, a sudden whack with suitably large hammer will free the jammed thread. Just remember the outboard end unscrews clockwise!
Have you tried heat, penetrating fluid etc?