Not sure where you are based, but @[Valdelisbmw] at Motor Confidence, site sponsor here, has done plenty of diff work, rebuilds replacement etc. recommended and worth a try!
EDIT: @[Peter-E36] on here has the internals of a 6 speed autobox diff from a 335i, not sure if it will fit the 320i but again it could be an option! I'm sure either members above will be more knowledgeable!