While I've still had no luck finding the disc that came with that scanner that's hooked to my newly rebuilt server, after turning the house upside down, completely reorganizing my software-and-tech-books shelves, and Siobhan cleaning her desk, there's a sort of happy ending. Poking around Visioneer's website looking for a contact address, I chanced to look at the Accessories page for the scanner. To my surprise, one of the items was another copy of the original CD, with the bundled PaperPort software, for a price of $0.00. You'd think they could mention this and link to it on the Bundled Software page where all they say is "you can't have it"!
Naturally, it's not really $0.00 because there's $9.99 shipping, which on the face of it is quite silly. I had to confirm my ownership with a serial number entry, and presumably this is what makes them able to send me the disc without too much worry that I'm pirating the obsolete version of the PaperPort software. If that works, why couldn't they just let me download the same thing? It's not like the CD is copy-protected so I couldn't just rip it if I were so inclined. Presumably, the $9.99 includes some profit, not just cost recovery, because there's no other reason that makes sense.
Doubly frustrating because I not only have the disc somewhere (though I think mine was red), I have a complete installation of it on my hard drive and also on a full backup I can't use. Still, $10 is not too bad, so I've ordered the disc, and in a week or two my scanner should be back in business.