This is more of a half*ssed observation than a real suggestion, but back when cheap consumer devices with ADFs were still rare, I noticed Fujitsu makes/made a bunch of industrial-sized devices. No idea if they're fast, but they appeared to be built like tanks.
VueScan is a pretty stable alternative to nutty proprietary drivers, though your dying-cat problem may not be software-related.
Edit: Oh, and probably out of your price range, but the Canon Imagerunner copiers at work sure can scan fast. Perhaps a surplus machine of that caliber can be found cheap on Craigslist or similar, though you'd still need somewhere to stand it? (Note that the Canons seem to require some funky 'MEAP' software licenses to enable certain features, so I dunno if they lock themselves down when not visited by a service tech regularly).
