Believe it or not, the problem appears to be with newer DVD drives, not with Win 7 or the disk or anything else we thought.
I've actually got it mostly installed by opening the drive and wiggling the disk every time it complains about a supposedly 'corrupt' file. Hitting retry then has gotten me almost all the problem files (Though there's one stubborn hold out that obstinately insists on not installing. In the interests of a full test, I finally ignored it).
I'd also like to add at this point that Larian have been hugely helpful and friendly in trying to deal with what is undoubtedly a very mystifying problem. They've done their level best to help me get to the bottom of this, and one can't honestly ask for more than that.
The game is now working, so I'll worry about the missing texture file when I come to the place it provides the graphics for. Hopefully by that point a better solution will have been found, anyway.
