I can't watch the video because I'm at work, but seeing as you said it is a J30 diff in the factory case, is it shimmed properly? When I swapped my diff I flipped around the shims on accident, it made some awful noises on my bench, swapped the shims and everything was perfect.
Like brndck said, check your driveshaft. If your carrier bearing is torn or cracked, thats probably your issue. Once the carrier fails the driveshaft can flop around and cause the u-joints to fail leading to all kinds of awful noise and vibration.
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