It seems the S1300 is a special case. I did look at several third-party options and none supported the S1300, while they did support other Fujitsu ScanSnap models.
I can’t help but thinking that the “bricking” of older models is a deliberate policy by Fujitsu. Because with every update of MacOS (or OS X) their software stops working and needs an upgrade. It seems they’re just building a version check into their software.
Anyway, it’ no longer an issue for me, as I definitely will never buy a Fujitsu scanner anymore.