Went back and watched your video again. Saw some familiar sights!! The Amway building for one.
No, I do all of my own work. I have never needed to rebuild a diff so I can't help you there.
But I can tell you that you can run the diff like that next to forever if you're willing to put up with the sound and change the fluid as soon as the sound changes.
Using a 85w-140 gear oil can really quiet down the noise.
A proper repair is a rebuild or a new diff. I can give you the name of a good auto salvage yard.
And the place that rebuilds i can tell you where commercial trucks go to get diffs rebuilt but not passenger cars.
All of this is assuming it is the diff going bad.
The way to test it would be to remove the rear driveshaft and with the truck in the air run it up to speed, is the noise gone? Yes? Remove front driveshaft and install rear, repeat. Noise still gone? No? Rear diff.
It could be tires. If it starte all of a sudden low tire pressure can make different sounds.
Could be the transfer case too.
It is really hard to say for sure by just the video.