While it didn't solve the issue, it *was* enlightening: the issue is explicitly with one particular household! Another household in the same save does not have that issue.
The household that it doesn't work with consists of three members: Izzy Fabulous who's in the same career as he is in standard, one Sim (the knitter) who's an interior designer, and one Sim that I imported from the gallery (currently unemployed, is going into Uni). She has what looks like most of the traits from the reward store, whereas none of the others have any.
They live in one of the Uptown apartments, next to the Fang family, whereas the working family lives in a house (and consists of a knitting child and a scientist).
I'm thinking I should test three things:
1) Repair the game with the save files not backed up
2) Teach the others to knit and see if either of them can add things into the wardrobe
3) Create a completely new savefile with an interior designer
Any other ideas on things I can try? At this point it doesn't look like it's a critical bug, but it's annoying and I want to do my best to ensure plenty of information for whomever's needing to hunt down this bug.