Here's a tip that I discovered along the way of the half dozen or so swaps that I've done so far.
The problem with guessing and checking with the shim under the pinion bearing, is that if it's wrong, you'll almost always destroy or damage the bearing pulling it back off to change the shim. So, buy an extra pinion bearing, and then grind out a tiny bit of the inner bore so that it will slide on the pinion without having to press it on. A little bit of drag is ok, but just make sure it will come back off pretty easily.
Now, you can use this bearing when setting everything up, and if the shim needs to be changed, it's easy to do so. Once you get it all dialed in correctly, press the real bearing on, assemble everything, and you're good to go.
I'm a BIG believer in the gear pattern. If it's not right, even if everything else seems to be within spec, they're probably going to make noise. So I always set everything up to get the pattern right, and then I check the backlash last. If it's within tolerance (I shoot for the top end), then it's ready to roll. If it's out of tolerance, readjust to get it in, and then change whatever needs to be changed to get the pattern back. Rinse, repeat, etc.
I also believe that a lack of proper carrier bearing preload is a bigger cause of gear noise than the gears themselves. You should have to drive in the last shim on the carrier with a fair amount of force; if you can pretty easily roll the carrier out once all the shims are in, then you probably don't have enough preload. It should be nice and snug in there.
I've done a good half dozen gear swaps now, and haven't had any problems or noise out of any of them so far.