Last resort time. Try a car jack.....put the nut back on so it has 3 or 4 turns on the shaft and then put on the matching socket on the nut. Now the tricky bit. ...place a car jack on its side and offer it up to the socket. Using load straps, tie / wrap the frame of the car jack to the frame of the bike. Use the jack to put pressure on the socket. Be careful and watch / listen for pressure stress. The jack may successfully force the axle spindle a couple of millimeters just to crack the rust. If it does then use the hammer on the socket or a drift bar.

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I have a lot of growing up to do. I realized that the other day inside my fort.