i have a 12l4 and was able to build the stock diff very smooth. i'll go thru what i do for you.
1-sand the rings with fine grit sand paper in a circular motion counter clock and clockwise. do this on a flat surface of course.
2-place the diff balls (12 of them) in the palm of your hand and place some lub on them (i use ae stealth lube). rub your finger over the diff balls spreading a thin layer over them.
3-insert them into the spur. then place a small dot of lube on the diff balls on both sides of the spur. don't overlube, you don't need much and too much will just attract dirt.
4-assemble the diff with new hub bearings. everytime i rebuild a diff i change the bearings. a bad outer bearing is the cause of a notchy diff 99% of he time. sometimes you can get away with just swapping the inner and outer hub bearings.
5 -slowely tighten the diff an eighth turn at a time. with each turn stop, grab one wheel and the spur and turn the other wheel a few times to break in the diff. then grab the other wheel and spur and spin the other wheel. tighten eighth turn and repeat. the diff should only be tightened untill you can't spin the diff with your thumb while holding both wheels.
the diff may feel a little tight at first but one run and it'll be light silk. unless you slam something with your right rear wheel blowing your outer bearing in which case return to step one and repeat.
also, everytime i rebuild a diff, i use new rings and balls in addition to bearings. i don't use carbide or anything, just standard steel stuff. hope this helps a bit.