OK, I've solved (more or less) the cross-feed, it's now got about 2 thou' backlash in the middle and pretty much zero at the ends, which is doubtless down to wear in the screw.
The next thing to receive attention will be the slide ways. It's a more or less conventional dovetail shape thing, with 2 gib strips in one side of the slide. They're a bugger to adjust, but the biggest problem seems to be uneven wear, which means that if you get it tight enough to have more or less no play in the most-used area (about 1/3 of the way along) it won't readily get to either end, so you end up with a compromise.
So. Any suggestions for how to skim the mating faces to get them back parallel? Obviously, there's some adjustment to be had in the gibs, or indeed they could be replaced; but there's not much point in that unless the main surfaces are parallel.
The cross-slide comes off easily, the saddle probably not so easy, although obviously it comes apart somehow, and I don't doubt both need attention.