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IMO it’s none of the three things you mention. Rather just shitty threads on the axle and nut. And maybe wear to the knurling on the locknut.
Mavics do it a lot, American Classics are terrible for it though they have a slightly different, female axle/bolt set up.
New nuts might help, new axle and nuts and lock nuts probably the best way to sort it.
If you can figure out the axle thread diameter and pitch then you might be able to find an lbs with a die or just buy one off eBay. That and new nuts maybe the most cost effective?
First thing that came to mind was broken axle. Then reading your reply, second thought is bent axle, third is very badly seized bearings.