I'd suggest getting the backlash somewhere in the ballpark and doing a test drive to see how much noise you end up with. If you don't see a fire engine in your rear view mirror, it's possible the siren behind you is actually the rear end gears! Seriously, a little gear whine doesn't concern me unless it's coming from a brand new gearset I've spent a lot of time trying to get exactly right. I listened to a whine from a Dana Type 60 in my 59 Burb all the way from California to Tennessee, and for a couple of years after the move. The backlash didn't change in about 5,000 miles, but it was a little noisy all that time. That one had a GMC housing, Ford gears, and Dodge pinion flange- - - -all junkyard parts!
Jerry