Okay, well, this is about 5 years after I initially expressed my intention to read the fic, and even at that it was pushed up the queue for various reasons, but regardless, here we are.
Given I spilled a lot of ink on the idea of feedback and how it should be given, time to put my money where my mouth is.
As you have been informed from all angles, the writing, qua writing, is solid - logical progression, general internal consistency, etc. But, as I'm sure you're aware, it's far from perfect.
I won't say that these are flaws per se, but I would certainly consider them areas for improvement:
On a tonal level, I'm afraid my own ability to convey my sense is somewhat limited, so please forgive me for speaking in mildly synaesthetic terms:
Hisao, Iwanako, and their old school are greys - urban, formal, routine, businesslike, urgent,
normal. Yamaku and its denizens are colorful - rural, familiar, unpredictable, casual, laid-back,
different. Hisao reacts to Yamaku by acquiring his own color; Iwanako, being an anti-Hisao, clings to her greyness.
Right off the bat, I'm struck (and not in a good way) by Iwanako's ready comfort with being on a first-name basis with near strangers. I'd expect her to be uncomfortable, or even irritated by this breach in protocol - she should be addressing them (and even thinking of them) in terms of their family names - "these people aren't my friends, and I wish they'd stop pretending they are."
This becomes a larger problem when there's no real tonal contrast - Yamaku should be
different from back home. Home is grey, the hospital is grey, but Yamaku is colorful. Unfortunately, on the macro scale, much of the time you cover at Yamaku is just as grey as the hospital. This is a big point, so I'll get back to it in more detail. I will grant that, on the more personal level, you manage to achieve this sort of color contrast - all the scenes in Yamaku that feel "colorful" are pesonal interactions - Iwanako talking to Misha, Lilly and Hanako visiting Iwanako, Iwanako swimming with Aoi and Keiko, Momomi's criminally short scenes. Even the character of color is generally on-point: Misha, Shizune, and Momomi are jewel tones - bold, uncompromising, and a sharp contrast with grey; Emi and Rin are pastels - a bit softer, a somewhat acquired taste, but still contrast strongly with grey; Lilly and Hanako are earth tones (chromatic greys) - soft, gentle, and perfectly at home with grey.
The first half of the story especially (i.e., up until Hanako's visit in the hospital) simply has too much of this grey.
To build on this, I want to return to my earlier comment: while everyone else seems solidly in-character, one character from KS is depicted wildly out of character - the school itself. Your Yamaku is downright hostile and unwelcoming. This wouldn't be an issue if the unwelcoming aspect were all inside Iwanako's head (in fact,that would be a vast improvement); the problem is that you include objective evidence to confirm Iwanako's paranoia.
You are correct in noting that smaller, more insular communities are full of backbiting, innuendo, and suspicion of outsiders - often far more serious than the casual facelessness and insignificance of the city. But a key feature of this internal venom is that it's strictly internal. To the committed outsider (i.e., not an outsider trying to become a local), all they see is a big smile an "Y'all come back now, ya hear?" You never give Yamaku this friendly face. Iwanako may feel like everyone's staring at her, and there's no question they are, but they would never
allow her to notice that they're staring. They're all smiles and "No need to be so formal, call me by my first name!". As I said above, "colorful." Iwanako's alienation shouldn't come from everyone seeing her as an outsider - it should be from her
feeling like an outsider. Unlike Hisao, she doesn't
want the color - she wants the comfortable greys she's had her whole life. To use your "Hisao-shaped hold analogy", your change in the behavior of the Yamaku students departs from the concept of a space that's perfect for Hisao in which Iwanako doesn't fit, and changes it to a "not Iwanako-shaped hole" - a space that is
actively, rather than just passively, inhospitable to Iwanako.
In other words, if the idea you're trying to express is that Iwanako can't fit into Yamaku the way Hisao can, you can't derail Yamaku's open and welcoming facade. Iwanako's alienation needs to be because of Iwanako, not random chance or coincidence. Other students stare at her because she's a mid-year transfer student, not because she's dressed differently, but they did that to Hisao as well. The only reason Iwanako would "notice" is because she's imagining it, because she's self-conscious of her different uniform. Shizune gets frustrated with Iwanako's helplessness and suggests Mutou get involved, but she shouldn't give Iwanako the cold shoulder; Iwanako should try to minimise interaction out of fear that Shizune hates her (Shizune hates lack of effort/laziness far more than incompetence; the latter isn't necessarily the person's fault and can be helped).
And then we get to Iwanako herself. As you previously noted, she's the Anti-Hisao - Hisao likes books, Iwanako likes movies; Hisao's good at Science, but bad at History and English, Iwanako is good at History and English, but bad at science; Hisao likes girls, Iwanakao... also likes girls.
Now, it appears to be your intent, but Iwanako's a bit of a shallow egotistical unlikable bitch. That's all well and good, especially since character growth seems to be a goal you're working toward. Unfortunately, she seems inhumanly bitchy. As I read, the question increasingly came up: "Is there
anything that Iwanako likes? And the answer came back more emphatically each time: No. She was part of the Tea and Ikebana Club, but it wasn't anything she really
cared about so much as an inoffensive way to pass time. The same with movies, books, etc. We get an ever so mild implication that she
might like animals/pets, but nothing concrete. She doesn't even have the slightest lament about missing some activity that used to bring her joy. In fact, the only thing she seems to care about
at all is her appearance. To some extent, that could be chalked up to depression, except that means she's been depressed
literally her entire life.
On top of that, we get to the issue of language as it refers to Iwanako's internal monologue. I love sesquipedalianism as much as the next pedant, but the fact remains that words have meaning, and (a point I often emphasise) narration is a manner of characterisation. In Iwanako's case, there is a disturbing tendency for her to use fancy words as a way of describing individuals with a clinical detachment. This came into relief most severely when Emi was described to have a "lachrymal" face - that's Patrick Bateman levels of emotional detachment. As such, especially in combination with the previously-noted issue of no actual likes, Iwanako's erudition begins to paint her as a sociopathic misanthrope. Given her near-obsession with keeping up appearances, it's almost like a body snatcher trying its best to pass as human. Add on the fact that the only human emotion we've really seen her express is anger, and Iwanako comes off as far more disturbing than I think you ever intended.
Finally, it's a little trivial in relation to the other comments above, but something that struck me about her second hospital visit is that a concussion, especially in light of the expressed symptoms, would categorise Iwanako as a Major fall risk - she wouldn't be allowed to get out of her bed (even to use the bathroom) without assistance. While I'd normally say that such logistical considerations don't need 100% adherence, this is a case where the restrictions would only serve to enhance the helplessness and isolation she feels, and there's little to no instance where freedom of movement would be relevant to the plot - if you're gonna put a character through hell, you may as well take advantage of all the tools available to you