i had really hard time when I did try to lube the splines last year,
the issue i faced was using the nut method remove and re-install the stud, the nut were not up to the quality( tried buying from 3 different sellers) and kept slipping on me and i started having a lot of issues, i kept ordering nuts to match the stud thread size but they didnt, barely few of them matched and i was somehow able to finish it,
unless I find a reputed stud remover and install kit which will fit the thread size on this differential stud I am not touching that.