Something you might consider,

Go underneath with a spray bottle of water. Spray one part at a time and see which makes the noise go away.

I would start with soaking the u-joijts both ends.and see if the noise is still there.
If after you spray the different parts and it still is there ,it may be something not related to the differential at all.

It might seem like a little work, but is a good way to eliminate areas one at a time, what do you think?

One other suggestion, pull both rear drums and see if you don't have a broken brake return spring getting ground up in the drum.