I can conceive a bunch of potential methods for shining a light through a slide and taking a sufficiently high-resolution in-focus image, but there may be unforseen pitfalls, so a known "this will work" solution would be great.

The information is very likely out there somewhere, but trying to search today's web is far too frustrating.

If I can get something that's a constant white, maybe the least painful option would be tripod with a macro lens, and clamping a ruler so there's only one dimension of alignment to deal with.

I guess the question would then become how much does one need to pay to ensure the light is sufficiently diffused - are the cheap illustrator-targetted options good enough or would they have a subtle pattern when photographed.

According to Andrew Clifforth, it's the latter, but a good diffuser can overcome that, however they want £65+ and 17 working days to send out some plastic. :/

Nikon do one, though obviously it has an uncommon thread size... I think it'll fit my Sigma 30mm f/1.4 EX, and of course it's £150/160 new, or £115 from the nearest used/refurbished shop, where I could physically confirm it fits, and test whether my extension tubes allow close enough focusing. That's still a fair amount of money for a few bits of plastic.

For a similar price there's a Kenro 302 scanner which can be used standalone and outputs to SD card - though is only 8MP JPGs instead of the cropped 16MP NEF raw files my camera would give, but would probably still be good enough.

But then, I do have a diffuser already, so if that can sufficiently blur the pixels of a bright white screen (I need to go get it and test), then the rest might be tedious but ultimately solvable.