https://youtu.be/B4LBlyiKElQ
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I have the same machine, have to made the video about sorting the back lash on that cross feed. Mine about 5 mm. Do not think it is only the nut because the pitch is about 5 mm. Perhaps a spacer is missing. What about to modify the nut to take up the small free play as it wears. Like you mentions all the chips gets blown on to the lead screw and then that keyway acts like a cutter.
Also like your DRO set-up. Is it on the chuck side. Where did you get it and what make is it? Looks and sounds like you from ZAR.
I am from ZAR (Gauteng). I bought Sino scales and a Delos DRO from CFP Technologies in Pretoria. On my machine I know the nut is machined with a loose tolerance. The leadscrew does not move as I have made custom hubs for the thrust bearings and there is no play there. In the video you can see how loosely the nut fits over the leadscrew. I am still thinking on an approach of maybe making a custom anti-backlash lead-nut. The tensioner spring provided just doesn't cut it. A friend of mine re-made the lead-nut and reduced the backlash to 0.1mm whereas mine is currently at 0.7mm. A work in progress. :D