I'm curious if there's anything else you want me to test beyond "wear it down some more" in an attempt to make it more consistent for troubleshooting purposes like go out for a long drive. Other than waiting for it to fail there's the nuclear option of changing axle and differential bearings but that's not a fun job if that's not the issue.
If it were me, I'd start simple and cheap -- pull the wheels and drums to see if anything seems obviously amiss. It could be something simple, like a brake shoe hold-down spring or something has failed.
You'd get to see where the axle passes through the seal and see if an uneven wear shows up on the shaft where it passes through the seal, then push/pull on the shaft for abnormal end-play, and twist the hub-end back and forth to make sure that the splined mating between the hub and shaft is good. If you suddenly got 20-deg of rotation instead of the normal <5-deg, well, obviously there's a problem in the axle internals.
While you had everything jacked up, and tires still on, you could take a gloved hand over the tread surface of the tires while spinning the wheels to see if any high spots are present, implying that a belt in the tire could have failed.
I wouldn't consider tearing into or changing an entire axle out entirely until I had done some very simple checks first.
Good luck diagnosing...
David