I took my Nexus 6P to fonebitz in the Old Bank Arcade a bit over a year ago when it was having the shutdown problem. They had a new battery installed and the phone ready to go in about 4 hours, very speedy. And they charged me $5 less than they quoted. Their repair page (which I've linked to) says they tackle water damaged phones.

Have also used them. Good service. They have a second store too in Willis St (between Manners & Bond).