Update: I fitted the disco pads and they were great... for five days. After that, the squealing crept back and is now as bad as ever.
So, here's my next step: I'm replacing the calipers just in case there's any leakage contaminating the discs. I sanded them (and the pads) thoroughly at the weekend again but within a day the noise returned and I have a very fine black film on the discs. I don't know if that's normal road film that accumulates or something else.
Although the new calipers come with pads fitted, I'm going to order a set of superstars too.
What I'm still trying to decide on is: do I buy new discs too and fit everything at once?
It's really pissing me off now.