The differential isn't mounted to the body. It is mounted to a subframe that has three large rubber mounts; two at the sides in front of rear tires and one at the rear cover of differential mounted to the center. If any of these mounts are too far compressed the noise will transmit so much easier.
Even with new mounts the differentials were noisy as the area under the package tray acted as a speaker to amplify the noise. As I was replacing a "noisey" differential under warrantee in 1975 the factory rep who had to OK the job told me about a dealer in Texas that filled the area under that rear panel with the hardening foam that turns to insulation. He said this made a big difference. I have never tried it. But, I would definitely see about the mounts before worrying about the differential.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician