The first thing that comes to mind is the wheel bearing. Does the noise get louder when turning right? If so, that would tend to confirm it. I'm surprised you didn't find gear oil leaking out---or maybe its still at the stage of oiling the parking brake and hasn't become obvious yet.

They are kind of a nuisance to change---you need to pull the axle shaft, cut off the old bearing, and its retaining ring, then press the new parts on with a shop press that is large enough to take the entire shaft vertically, and a piece of pipe of suitable length and diameter. The bearing has to come off to replace the axle seal, so plan on a new one of those too, while its apart. Parts used to run about $50, but that was a while ago.

The quick and dirty alternative would be to swap in a complete shaft from another axle, and hope the bearing and seal are OK.