Hmmmm.......you may have another problem nobody seems to address or talk about when it comes to backlash in used ballscrews.
The problem with a different screw, the Acme thread one is that the screw is soft and wears in the middle where the most action happens leaving the ends in almost new condition.
To take up the slack in an Acme thread you use a jam nut that backs against the main nut and so eliminates the slackness caused by the main nut wearing......it's a sliding fit and sparsely lubricated at the best of times,........adjusting for wear in the middle makes it tight at anything past the middle, so the adjustment is as close as the drive will tolerate and still move.
With a ballscrew, if you get backlash the first thing that comes to mind is the balls have worn......never the screw????
It is quite feasible to think that if you get any backlash the screw needs replacing period.
Fitting oversize balls means you will get a tightness at the ends or progressively past the centre point that puts a load on the stepper motor also progressively which means you don't notice the tightness if the centre part is now OK.
Having to eventually come to terms with this predicament made me think that the answer is to add another ball nut to the screw similar to the jam nut method used in Acme threads.
The design is simple, just screw another ball nut onto the screw, (if you have the room lengthwise for travel), with the flanges of the two nuts facing each other......one nut will be in a housing attached to the table, whatever.
Then fit threaded studs through the bolt holes in place of the original cap screws and pull both nuts together with NYLOCK nuts to prevent them from vibrating loose.
Once they're adjusted they will eliminate the backlash without having to think about odd balls and worn screws.
A lot depends on the overall amount of travel you have with the screw as you might lose some....the thickness of the second ball nut, or 42mm, but it's a simple fix.
Ian.