Something similar, but different application:
Sometimes when rebuilding disc brake calipers, the pistons won't come out. There's no way to pound them out from the backside, and air pressure didn't work. Threading in a zerk fitting to the inlet and pumping the cavity full of grease always gets the job done with no excitement. Clean-up is a little mucky, but not a big deal.
If it won't shoot out, won't ram in, compressed air failed, pump it out.
The best solution I've heard of as far as using a ball puller, is the one that drills a hole in the lead, then threads it - possibly with a self tapping bolt, and then pulled that way. If the ball is horribly jammed, that's the only solution that makes sense as far as ball pullers. But even there, if the ball is really stuck, I'd be concerned the threads would pull out. Then you'd be stuck drilling with larger and large drills till it's mostly gone and ramming out the remainder. I think the easiest, if air and shooting don't work, would be the application of hydraulic pressure via the grease gun approach.