You said you just did a rear diff fluid change... was this before or after the problem happened. If it was before, I'd go back and drain the fluid into a clean pan so you can see if there is any signs of metal in there, or worse if the fluid was lost somehow. (I recently replaced the rear diff of an E46 that had the fluid changed at an indy out of state, then drove over a thousand miles to La with the drain plug loose and lost the fluid. the diff was TOAST)

If the rear diff fluid is good you should take a small sample of the trans fluid to analyze as well. (a couple ounces) Also, If one of the rear bearings is going out and has a bunch of slack it can cause grinding noises and real weird brake feel, but you would know if that was the case... I suspect the rear diff myself from listening to the video.

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