Regarding your question of what diff grease to use, it might not hurt to try full synthetic. If that doesn't work or it starts leaking by the seals then just change it back to what you were using.

My 1989 260E with 100,000 miles recently developed a similar "roaring." Actually, its more of a low airplane propeller sound. The mechanic took it for a drive and the sound went away while turning the car to the right, thereby indicating it is the right rear wheel bearing. He said he doubted it is the differential because the sound of the differential is much less when travelling at a constant speed. According to him it is unusual for a rear bearing to go this soon. Any ideas what would have caused this? Maybe an accident or a problem with the axle? Would this be noticeable from just looking at it?