Resolution!
Preface: I guess I should have mentioned in my first post that a local shop that has done some brake work on the Burb replaced the axle, carrier, and ring and pinion bearings, axle shafts, and axle seals in the rear end in mid-February.
Short Story: The noise was caused by improper backlash in the rear differential gears and the shop responsible for that mistake has corrected it.
Long Story: Following my last post above, Trav and I exchanged PMs, he told me it looked like it could be a bad carrier bearing in the front diff on the driver's side. Doing some reading up on the intricacies of a GM 8.25 IFS bearing job, I decided that was way over my head to do myself so I would have to have a local shop do it, send it out for a rebuild, or swap it out with a junkyard unit. I called the local shop that has worked on the Burb before and initially diagnosed the noise as a bad wheel bearing/hub assembly (which I replaced on my own) and they gave me a quote of $1,000 for a front diff bearing job. I called a drivetrain and differential specialty shop a bit farther from me and they quoted $750 for the same work and $950 if the ring and pinion gears were damaged and needed replacing, but was told that they replace the R&P only as a last resort because they prefer reusing the original gearset. So I used some free rental days with National to rent a Suburban for two days for $4(!), dropped off the Burb at the diff shop on a Wednesday, and promptly left for a business trip.
I got a call from the diff shop the next day and they said the front diff was fine but that the bearing caps in the rear diff were reversed and the gear backlash was way too loose, which was the cause of the noise I thought was coming from the front end. They said I needed new bearings and new ring and pinion gears, which would run me $1,100. I called the local shop and they said that they would fix the rear diff under warranty if they concurred with the diff shop's diagnosis but would not reimburse me for the work if I had the diff shop do it. So I picked up the Burb on Friday (it was a short business trip), paid the diff shop $85 for "servicing" the rear diff, and dropped off the Burb at the local shop the following Monday.
Got a call on Tuesday and the shop's owner confirmed that the bearing caps were reversed and the backlash was loose, both of which he said were absolutely the mechanic's fault, but he said that the bearings and R&P gears were not damaged and could be reused with no issue. To help set me at ease, he reset the warranty for everything in the rear end and extended it from their normal 24 month/24,000 miles to 48 months/unlimited mileage. Also, it is a nationwide warranty, which is good because I may be moving 450 miles away in the coming weeks.
The car was finally ready for pickup on Thursday, with the long lag being because they had to order a crush washer and pinion gear seal from the dealer and they test drove it multiple times to make sure they got the backlash seat dead-on (put on 22 miles while they had it). I headed over but had to wait a bit because the rear diff was leaking so they were pulling the cover and re-sealing it. Since the cover was off, the shop owner invited me back to show me the open diff. He pointed to the bearing caps that had been reversed and gave me a good look a the ring and pinion gears so I could see that there was no scuffing or other damage to indicate that they needed to be replaced. As a gesture of goodwill, the shop owner gave me a $100 gift card to use for my next service there. They sealed it back up (using "premium" synthetic fluids, per the shop owner), gave me the keys, and off I went, with the Burb running quieter than it had in quite some time (I was driving on bad carrier bearings in the rear for several months)!
I have very mixed feelings about the whole ordeal. I am not too happy about having spent about $150 to do the wheel bearing/hub assembly replacement myself (although having an excuse to do some car work that is within my skill set was nice), using two free rental days so my family of 6 could still get around without the Burb, spending quite a lot of time shuttling vehicles around, being without the Burb for 4 days, or the $85 spent for the diff shop's diagnosis, but I am happy to have our primary family vehicle back on the road and running as strong as ever, appreciate the goodwill gesture of $100 off my next service, and thankful that the local shop offered to pay for a rental car if needed (I didn't take him up on the offer because it would have been more hassle than it was worth). My wife was ready to dump the Burb and replace it with something newer, but we are not exactly in a financial position to do so right now.
However, with not having to have spent the $750-1,100 we thought we would have to lay out to get things straightened out, it looks like it may be time to upgrade the Burb's stereo head unit and upgrade to Amsoil SVG for both diffs!
