What brand friction modifier did you use? Back when I was a Ford tech, I had replaced the differential clutches in a Ranger rear end and the parts department did not have the Ford brand friction modifier so they outsourced some off brand from the local parts store. Well, two days later, the truck came back with the chatter and by then we had the oem stuff to put in it. After the oem modifier was installed, the chatter went away completely.
I have done some D/C limited slip rears too and used the D/C friction modifier and it comes in the exact same bottle as the Ford stuff and smells the same awful stench. The only difference I noticed was the writing on the bottle; one says Ford and the other Dodge/Chrysler