Harmonic Howling? Just called in a major work order on the car: Diffierential work is strange but needs to be done

 : When oil and lubricants leak from the differential gaskets, it can create a harmonic "howling"
So I just asked for the rear differential gasket seal to be replaced (vid of dude making his OWN gasket seal) and to replace the differential fluid on both front and rear - and also to look at the spline on the front passenger side to regrease it! vid of a differential operating!

 I am amazed you are running this with out the bearing caps installed. The danger out weighs the contentI am amazed you are running this with out the bearing caps installed. The danger out weighs the content

So we're talking about the problems on the front differential design:

That type of spline needs to be cooled and flushed free of debris by fluid...the grease doesn't get it done and doesn't handle the pressure. Bad design choice for spline lubrication

This is a bigger engine with the same "differential bolted through the oil pan" design (on the bottom)

So it's a bad design since the front differential goes through the oil pan!

the passenger side intermediate shaft that passes through the oil pan.

the splined connection between the jackshaft and the bearing housing on the passenger side of the oil pan.

Again a much bigger engine but same design - the oil pan here is cleaned out and you can see the gasket seals!

I saw some images of this but still not quite sure....

  I suggest that every 20,000-40,000 pull the half shaft [axle] and add some GP4 grease.

The good news is that the bearing assembly doesn't need to be removed from the oil pan to determine if the splines are dry. You just need to get the cv drive axle out of the way. That procedure is essentially the same as most front wheel drive vehicles. I removed the brakes, upper two bolts for the shock/spring assembly, outer tie rod end, upper ball joint, and lower ball joint...in that order. Then a quick slap on the inner tripod of the cv drive axle gets you to the splines.

So we've had the sway bar end link replaced a couple times already but it's standard for them to rust out. Hopefully we can save the differentials since the differential fluid has only been changed ONCE on this car and they've been leaking.

you have to remove the axle on passenger side and there should be a bracket that holds the shaft in place. You would need to unbolt it and pull it out.... If you can't pull it out by hand, get a rag, towel or something to wrap around the end get pliers or vice grips to get a hold of shaft and pull which should be easy enough to get out. The towel is to keep the splines from getting damage when you use the pliers or vice grips.

The new mechanic we had was overwhelmed with work since he had to take on all the cars from our previous mechanic after the station owner shut down the repair shop.

 Second, check the outer seal and CV tripod for wear or excess movement...

https://offroadtb.com/4wd-disconnect-rebuild/

 These differentials are designed like a lawn tractor part. Total junk even in like new condition. They will fail not a matter of if, but when. GM should be sued for making this kind and crap for so many years.

 If the tire can not be plugged - then all four tires will have to be replaced since it's four wheel drive. So that's been down twice before already on this car.

 just remove the drive shaft then remove the flange by removing the nut and washer. Once you do that you will be able to remove the old seal and replace it with the new one.

The car has an automatic four wheel drive sensor and then the driver does not know when they are in four wheel drive....

I believe that the root of this problem (besided the inadequate spline length) is the AWD "software". If you have a limited amount of wheel slip the AWD engages gradually and it works really well and most of the time you never even know it is engaging. The flaw in their "software" is that in really slippery conditions the AWD engages really hard and you get a loud clunk when it engages.

 So I have no idea what will happen. Because of the above design - the bearings have to be regularly replaced - when I was using this car to deliver fruit (with it full) - then I got the bearings replaced a couple times.

 First, engage 4WD when traveling at slow speeds.

But luckily I don't keep the car in the automatic sensor system. I just keep it in two wheel drive and then switch to "locked" 4wd when I need it - going into the EcoEcho Forest Cultivation site. So it's more sensitive than I realized.

splined connection between the jackshaft and the bearing housing on the passenger side of the oil pan.

The mechanic just kept saying "OK" as if he understood what I was saying and I kept talking as if I understood what I was saying - even though I really don't. haha. So he didn't think it was a problem to get all this work done!

Your front diff is on the driver's side of the oil pan. There is a CV axle that goes to the drivers wheel. There is an "intermediate shaft - IM" coming out of diff, through the oil pan, to a carrier housing that attaches to the passenger side of the oil pan.

we shall find out?

My experience is the carriers need to be opened up anytime after 50k miles. If you wait too long, the thrust washer will spin into the housing and it isn't salvageable.