[Hib Halverson]

What you do next kinda depends on how much work you want to do.

One choice would be to take the car to another rear axle service facility and either give them a ride or let them test drive the car then ask their opinion.

Another would be to buy yourself an automotive stethoscope, get the car up in the air and support it by the rear knuckles so the half-shaft angle is not too severed then have an assistant run the car in 3rd or 4th gear with you listening to the axle and/or the trailing arm bearings so see the specific source of the noise, ie: pinion bearings, side bearings and so forth.

Be careful of that hot exhaust.

The last choice would be, if you have access to "Picoscope" equipment, which is what GM dealers use to diagnose noise complaints, and that will quickly pinpoint the noise problem.

I'd say you have a 90% change the problem is in the axle and 10% something else.

A prop shaft balance problem will make a buzzing vibration you can feel and in some cases hear.

Finally, there are a few just plain "bad" gearsets out there which make noise and cannot be fixed by gear set-up.

Whatever it is, if the hum is that loud, it's going to be something major and quite obvious.