His power will be working with his limitation in place! He may only get through so many doors, though, so to keep it "fair" and let everybody else get a shot, we may limit the amount of doors York phases through to about three or four. And unlocking the door will still be necessary in order to access what is properly inside -- York phasing through will not unlock the area/room/etc for the entirety of the Circle.

Be careful not to get stuck, though, because some doors are harder to open than others, and someone may need to break down the door to get you out if you run out of time. ;)