My view of the chronological order of Jinrui wa Suitai Shimashita episodes
(There are some semi-spoilers for Jinrui here, but this is deliberately mostly opaque if you haven't actually seen the show.)
I'll put my conclusion first and then write on about my justifications later. Based in large part on Vance's comment at A&V, my assumed chronological order of episodes is: the school portion of 11-12, 10, the epilogue of 12, 7-8, 5-6, 1-2, 9, and ending with 3-4.
There is a clear ordering of some episodes: the school portion of 11-12, 10, 7-8, and then all episodes with the Assistant (1-2, 3-4, 5-6, 9) in some order. It's strongly implied that 1-2 follows shortly after 5-6, since Watashi's hair is cut at the end of 6 and episode 1 is the only other episode where she has short hair (and she returns to long hair before the end of the episode).
(Although I think the ordering is sensible, I don't think the show supports Vance's logic about the relative positions of 9 and 5-6. In 6, Watashi is rationally afraid because she's around a bunch of angry people who are upset over what she's deliberately done; in 9, her screwup is mostly accidental and pretty much private.)
The position of the non-flashback epilogue of 12 is not clear to me. It has to go after 10 (since Watashi has fairies) and before 3 (since the epilogue is the first time since school that Y and Watashi have seen each other). I think it can't happen shortly before 3 since the dialog between Y and Watashi in 3 implies that it's been a while since they saw each other. Based mostly on Watashi's relative equanimity in 7-8 onwards, I prefer to put it between 10 and 7-8.
It makes both internal and thematic sense for 3-4 to be the chronologically last episodes. In internal logic, 3-4 is where Watashi is the most hands-off and concerned about the fairies and their enthusiasms (an attitude that makes sense for her to have after 9). It's also where the faeries are the most overtly weird and ostentatiously magical in what they do. And, as Vance mentions, it's set in winter or very early spring, unlike all of the other episodes. Thematically, 3-4 can be read as a meta-commentary on the show itself and episode 4 climaxes with the characters' (manga) series being canceled, the characters waking from a dream, and so on. Applications to the end of the anime series itself are obvious.
(Read this way, many of the lines at the tail end of 4 can be given double meanings. Consider Watashi's line that the fairies' mangas are too hard, for example, given that Jinrui itself requires work to understand at more than a superficial level.)
I have no idea what chronological order the original light novels are in and I'm not sure it matters. I'm inclined to consider the anime a separate creation from the LNs instead of an attempt to adopt them literally. (The things I see in the anime may be there in the LNs too, but I'm not assuming that. Jinrui feels like something where the anime may have gone in its own direction.)