Most ring gears and pinions are marked with what the pinion depth should be. I have set up a few ring and pinions in my time. I have a pinion depth gauge that sits in the saddle where the ring gear goes reaches down and measures the pinion depth. This is critical to having a quiet gear set. Obviously after the pinion depth is set then the clearance between the ring gear and the pinion must also be set. But it sounds to me like you are using the same ring and pinion as you had before the bearing noise. If that's the case then maybe the bearing is installed and properly are too tight. Does his have a crush sleeve? A few things to consider.