Wow it does work!
Interesting, according to my first math on it the modified BS is right! I did an empirical simulation for the dealer outcome and probability using an infinite deck model of what happens when you draw one card to a 13.
H17 game, player has 13 vs. dealer 2-
Player advantage without push-22 rule-
Stand= -28.66%
Hit= -30.89%
Player advantage with push-22 rule-
Stand= -43.88%
Hit= -40.25%
So I guess it does work. But it's very counterintuitive, being that if the dealer is going to get a 22 there's nothing you can do to improve your hand, you can only make it worse.