If, with BIH, you can't hit the low-ball directly, you're not on a foul and the 9-ball is hanging, I'd say you have a firm grip on your opponent's nuts. Pocketing the 9-ball only loosens your grip. No matter what, an advanced player is still the strong favorite to win from here but your opponent should be more interested in removing the 9-ball from the jaws of the pocket than you. I would take BIH, deliberately foul by tying up the low-ball even more. If you couldn't hit the low-ball, he should be incapable of doing it too and with BIH, he'll be faced with the choice of deliberately fouling to open-up the 1 WITH a hanging 9 or leave the cluster, put himself on 2 fouls and spot the 9. I'd say that's checkmate.
I will certainly acknowledge that the scenario I laid out has the pusher in the more powerful position, but unless the 9 is removed from the hole, passing the shot back leaves the possibility of a magical shot, like jumping onto the top of the ball and somehow contacting the 9, resulting in a win for the first fouler.
Removing the 9 eliminates the miracle shot's possibility of an immediate win, strengthening the pusher's position further...and IMO, significantly. Like from 95 to 98% :wink: