Here are a two modifications in one post:
As delivered there was more backlash in the cross-slide than I liked, and the first time it started creeping up it took a while before I noticed that the screws holding the lead-screw nut were slack. After tightening them, the slackened again; and again; and again ... Striping it down revealed one of those nasty push & pull arrangements (I hope there is some suitable torment in the afterlife for whoever it was that perpetrated this design).
I bit the bullet, did some careful measuring, and made a shim so that the nut could be screwed hard to the cross-slide. That didn't work so I got the shim thickness right by trial and error.
Another problem is lubrication, because the lead-screw is inaccessible without dismantling stuff. The answer to this was to drill a small hole into the nut where the middle screw of the push-pull arrangement would normally sit. That was opened up to a by-eye depth by the first right-ish looking drill that came to hand to form an oil-reservoir. Now all I need to do is, from time to time, remove a blanking grub screw that keeps the muck out, and apply my trusty oil gun to the hole and give it a couple of squirts to fill the reservoir and replace the blanking screw. The lead-screw now self lubricates as I use it.
The other mod is still in progress. The backlash on my machine originates mostly in the flange in cavity arrangement that transfers the thrust from the leadscrew into the body of the saddle. The flange has to be smaller than the depth of the cavity so that there is clearance for the lead-screw to rotate. That clearance is the end-float.
My solution is to convert the thrust arrangement to a ball-race. That source of nearly everything, ebay, produced ball-races with a 10mm ID, 15mm OD and 4 mm thickness; just the right size and under £4 for 10! The mod is simple: Fix the bearing inner to the shaft (I'm using Loctite as the fit of the inner on the shaft was just shy of a hard push-fit) and fix the bearing outer to the housing. This will entail boring out the housing to 15 mm dia to suit. I'm pondering how to secure the outer; I'm thinking go for press-fit, but resort to Loctite or clamping as a Plan B if I mess up Plan A.
Ball-races are not designed to take large axial loads, but I'm pretty confident that they'll be OK in this application. They have to have internal clearances in order to work of course, but they will be tiny compared to the existing arrangement, and so I should end up with a nice smooth, easy operation with minimal backlash and no need to do any shimming. Picture of the work in progress below.
Watch this space.