@forecast
That's why you invoke absolute fear. You can control people through only two things: fear and love. It's impossible to make the mafia love you and as a lawful good, you don't want to be buddy buddy with the mafia anyway. So the only way left is to make the feel fear beyond what they can handle. In this case, Nietzsche recommends absolute cruelty once and only once.
1) Beat up all those thugs, throw a few into the sea, and interrogate the rest. If the thugs still won't cough up the location of their bosses, throw even more into the sea until one is wiling to talk.
2) Once you got the location of the bosses, you beat up the bosses and get rid of them permanently. A nonexistent person can't hurt you or anyone you care for. The will be no anger if there is no one left to be angry.
3) Sure there will be leftovers, some lower ranked dude who gets promoted because everyone above him is gone, but he will now know what Bei is capable of and will do absolutely everything not to attract his attention again.
Attacking the church or the kids won't raise anyone's ire. There has not been any indication so far that the church has any influence here. As for the kids, nobody cares, they're orphans squatting in the back alleys. Even if they're all dead, nobody in that city will care.
As for having higher-ups cleaning up the mafia, I doubt they'd do much good. If they could do it in the first place, they would've done that already instead of letting the mafia take control of the capital. It is safe to assume that the knights, princes or princesses are incapable of solving their own problems or they wouldn't have allowed things to spiral down to this point.