I rebuilt a differential before, but it was all shims which made it easy.

you need to clean all the gears really well, coat them with Prussian Blue (not too much), observe where the teeth are meshing, use a dial gauge and check all free play, etc.

wasnt hard, but then again it was just shim and torque to spec, I don't know about the audi diff (who even makes it?) but for the ZF differentials they use a crush washers on the input pinion to set end play and you have to set the drag (bascially how many ftlbs need to be applied before the output hub moves).

tossing bearings in there willy-nilly will probably only change the sound of the gear noise but not eliminate it, i would recommend swapping it with a known good used diff.