Have you opened up the differential and taken a close look inside at things?
If not, you very well may discover that if the pinion bearing is toast - the ring & pinion gears, plus the spider & side gears could be worn or chipped as well.
If this is the case - a complete rebuild including a new ring & pinion, spider & side gears, plus a new master install kit will be in order to "fix" it.
This will require pressing bearing, specific specialty tools & knowledge, & if a shop does it $$$.
If it were my Jeep & the D35 needed repair, I would toss it in the nearest dumpster & install a better axle for far less than it cost to rebuild the factory axle.