Sorry some Dynamic vibrations put me to sleep.

Not sure how successful it will be doing ballscrews on a small machine due to rigidity.
It also depends on how far under you need to go, a 12 mm diameter by 4 mm pitch will just clean up to 10mm but will still be on the hard part.
A 16mm x 5 will clean up to 12mm but again be hard, down to 10mm and you are into the soft core.

I rough down using old tips that have been licked on the top to give more rake, all I'm interested in is getting rid of material, surface finish doesn't matter. Once I'm close I change tips to a diamond coated, small cut to clean up and get a size then the ballance is taken off at one cut.

This is where you need a rigid machine as the tips are £49 each, no misprint and they don't do rubbing or light cuts.

Another alternative is to stub the screw, I have to do this for one customer as he uses 16mm ball screws but the bearings on the drive end are 20mm. On these I stub with a piece of 25mm turned down to 12mm and pressed into the end with some serious force plus Loctite plus a secret machining operation. The screw is then turned down to whatever diameters and threads to ensure concentricity.