Don, when I say "side thrust adjustment" I'm speaking to the adjuster bolt (that may be) on the right hand side of the housing when viewed from the front. It's on all HO72 and some HO52 Eaton units. You can see it in the image below.
Yes I understand there is an adjustment bolt. It goes in tight against the ring gear and then backs off 1/12 of a turn. I my mind this is a very strange aspect to have on a rear end. This should be set only after the backlash is set. Other wise it could hinder shifting the ring gear.
When I discuss the hum with other guys we all agree that the hum is from either the gears are to close and need to be opened or the pinion bearings are bad. Or at least this is the best place to start.
Thx Don