Hi....this is like sewing a new patch on an old coat......the ballscrew itself wears unevenly and if you only get .001" somewhere along the way after a refit that is phenomenal......you'll have to replace the actual screw too if you want perfection.
BTW.....reballing the nut will only make it tight in one spot and looser in others while the worn parts on the screw will still give you backlash
A double ball nut will not help with this problem as it's preload setting is designed to resist loading in both directions from the cutting force on a new ballscrew not as a wear compensator.
In cases where a well used ball screw is going to be put back in service you would need two separate ball nuts working back to back and a resilient spacer between them to prevent an over tight fit on the unworn sections and a slack fit on the worn areas etc.
Depending on the loading from the cutting forces the resilient spacer can be made from the hard rubber material used in tool and die work......the resilient material must be firm enough to resist compression from the ballscrew reversal.
Ian..