Ya that black piece will most likely be rubbing a piece of your driveshaft. If you jack it up it may not be touching at that time. So check where that black piece could possibly touch any part of your driveshaft. Mine dug a groove into it. Had the same symptoms as you, drove me crazy for a week. Maybe the new diff is a tad longer.

Bad diff in my experiences were a whining sound. Also a thud sound stop and go. Or a grinding if the gears are screwed.