The noise may be the pinion bearings. If they are trashed it's a little more involved, as far as removal/replacement. Might just be less expensive to locate another rear axle.

 

This is pretty much the nail having been hit on the head. I had a guy who has been fixing jeeps for 15 years drive it and that's what he said "Pinion bearing". He said it would be cheaper to replace with a used rear axle as the bearing race may be spinning in the housing, in which case the housing is fubar anyway.