Most of the methods suggested for re-placing the nut are only variations of the method that caused the problem in the first place.
An old old method of making a "shake-resistant" (as opposed to a "shake-proof") nut is to cut/saw it half way through at right angles to the thread and then compress or close the gap made by the cut in one of several ways:
- close it in a vice until it "sets";
- hit it with a brass/bronze "dolly";
- drill the outer part to be a clearance fit on a selected thread, drill and tap the inner part, fit hex or socket-head screw and shake-resistant washer, fit modified collar onto its original thread on (lathe?) spindle to required "torque", tighten socket/hex screw to suit.
To remove, just slacken off tightening screw and use "C" spanner or similar.
And no more need for the original problem screw or risk of damage to the spindle thread.
These methods are "oldies" but they work!!!