And seeing how two of my ideas have turned into stroies already (both by Eterya, so double thanks!) I feel inspired to share some more.

NERV Councilor

Have you ever thought: with NGE characters being problematic teenagers, why don't they pay a visit to a counselor?
So let's say Rei, Asuka and Shinji are just schoolchildren, there's no war with the Angels and NERV is the name of an organization that specializes on counseling problematic teenagers. The school which Rei, Asuka and Shinji attend hires one of NERV's counselors to work with the named three children. The counselor may be an original character or one of NERV staff from the series, say Fuyutsuki or Kaji. In his mind he may refer to the children by the order in which he read their files: First Child Ayanami Rei, Second Child Sohryu Asuka, Third Child Ikari Shinji. He invites them for counseling sessions in the same order, maybe a month between each session.
Rei's problem she’s clumsy at speaking with people, so the counselor says if she can’t use her words well, maybe she should use her body to interact with people or something along the lines. The point is for her to become a slut letting anyone fuck her. Maybe he gives Rei her first fuck to demonstrate how this kind of interaction can be performed by natural instinct and doesn't require social experience Rei lacks. Rei follows advice well and goes fucking people around. And it works as she's becoming more opened to people and no more aloof. She gets fucked by classmates without care that Shinji sees, and Shinji is fascinated by seeing it, it helps him realize how he loves Rei, but he still doesn't have a courage to approach her. What for Rei, she is happy now that she has no more problems communicating with people.
Asuka's problem is her egoism which manifests in her trying to do everything by herself and not trusting anyone to help her. Counselor suggests amputating all of her limbs. Asuka doesn't see why, but also doesn’t see why not. For one she witnessed changes in Rei after her counseling session and how it helped her a lot, so she believes the counselor knows what he's doing and lets him cut off her limbs right on place. Then he explains that the point is that in this state she won't be able to do anything by herself, not even feed herself in order to live. She will have to learn to depend on others. Rei is placed in care of her. At first Asuka hates her helplessness and feels degraded by how she can die of starvation only because Rei is too busy fucking all her sex friends and strangers and can forget to feed her. But in time she develops a deep bond with Rei and learns to trust her completely and to trust people in general. More that that, she comes to enjoy the fragility of her life, the way it can be over just by Rei's negligence. Rei often comes home late which makes Asuka thinks a lot of that possibility, and she discovers if Rei would be too busy with fucking to return and feed her and Asuka would die of starvation, she won't feel angry at Rei. This is the ultimate trust Asuka learned: she trusts Rei so much that in her opinion Rei doesn’t have to have a reason to leave her die of starvation (or do anything else with her), if Rei does it that that’s how it has to be. Asuka discovers that this way of thinking makes her at ease, so she’s happy to have learned to think this way.
Finally, Shinji. Seeing how the counselor helped Rei and Asuka and got him into realizing his love for Rei he is thankful and enthusiastic about receiving help for himself. His problem is that he’s afraid losing loved ones so much he avoids getting close to people in the first place. This is also why he doesn't have courage to start a relationship with Rei. Counselor states that in order to overcome fear Shinji must face it. And facing the feat means he must kill Rei with his own hands. As Asuka didn't see a problem in having her limbs amputated (at least until the counselor explained what it is for) Shinji doesn't see a problem in killing Rei in general. He brightens at a thought that just by killing Rei he can overcome his fear and stop being a wimp. But then he realizes he still is a wimp, so he doesn’t have enough courage to kill Rei. This vicious circle makes him depressed, but then Rei who was sucking counselors dick all that time stands up and tells Shinji that she loves him too and she wants to help him. She tells how happy she was when the counselor said Shinji can be helped if he kills her, because this meant she is in a position to help. Of course she’s totally unconcerned about her own death or about leaving Asuka to die by abandoning her. So Rei encourages Shinji to kill her, she kisses him with counselor’s cum on her lips. With her help Shinji finally finds the courage and does kill her, probably by strangling her right at counselor’s office. First moments after Rei's death Shinji is crying, overwhelmed by loss, but then, maybe with counselor’s help, he lets this feeling through himself and realizes it’s not as bad as he feared it would be. He finds that the feeling of loss it somewhat sad, but also beautiful in a way that it confirms he really did love Rei, and he certainly can live with that feeling. Shinji is happy to be healed of his fear, now he knows there’s nothing to fear in losing loved ones.
Without Rei to feed her, Asuka finally dies of starvation for real. Asuka doesn't care if Rei just forgot about her or intentionally left her to die - Asuka learned to trust Rei enought to believe that whatever the reason it's for the best, or rather there needn’t be a reason at all. Asuka learned to enjoy her state of not being able to live on her own, so she's only happy to die this way as it manifests this state. When Shinji learns of Asuka's death, he only smiles at losing her.

And here are some suggestions people gave me on this idea and my thoughts about them:
> I would pick Fuyutsuki as the councelor as I don't think Kaji would have enough experiance
Kaji did give some advise to Shinji in the NGE, so he does fit the counselor position. But that's really not important who would be the counselor - it doesn't affect the plot and it could be just some random guy.
> With Rei it would be good if you started her out slowly….like she goes to a gloryhole everyday after school and sucks guys off, then starts blowing guys on trains and then progresses to full sex at school.
That's how it's supposed to be, but it would probably be a short description of how she progressed to more and more perveted stuff rather than a detailed onw which would make the story longer than nesessary and shift the focus.
> In this story would Asuka be used for sex? like guys waiting for a shot at Rei start using her to relieve themselves….Maybe even borrowing her from Rei as part of her therapy, like she has to trust these strange men to bring her back home.
That sounds nice, again it probably wouldn't be too detailed though.
> For Shinji the councelor should encourage him to hump Rei's corpse when she is dead to solidify the idea…you know my necro fetish and all.
Hmm... I don't remember if I discardet it before, but now that I think of it again, this may fit. Like Shinji fucking Rei's corpse helps him accept her death as not an outright bad thing.
> When that is done he could go to where Asuka is and inform her that Rei is dead…then explain to her that as part of his therapy he will be watching he die, maybe he should masturbate or have sex with her at this time.
Not sure about this for now. First, my point is Asuka dying all alone (and enjoying it this way). Second, Shinji is cured enough after Rei's death, so his calm reaction to Asuka's death is supposed to only be mentioned to show that he's cured.

> As for the counselor idea, I don't think Asuka will have to worry about Rei coming home late. Rei's sense of duty will make her take the limbless Asuka with her EVERYWHERE, to better take care of the Second Children. Since "everywhere" will include places where Rei will be gang-raped, this means Asuka will be treated as a fuck doll, to be used and abused regardless of whether or not the Eva pilots gave consent. Hard core masochist that she is, Asuka will enjoy being fucked in the ass as her rapist forces Rei (who's also being fucked in the ass) to French kiss her.
Rei's therapy is essentially to make her more careless. Besides it might be part of her instructions not to place Asuka's needs above her own. So Rei doesn't care much about abandoning Asuka, essentially she feeds Asuka only when she's home anyway so that it's not much of a bother this way. But she won't return home just of her sence of duty and care of Asuka. She will only return when she herself wants to return. In the end when Rei encourages Shinji to kill her, she doesn't even think of Asuka.
What for using Asuka for sex, that was already mentioned before and sounds nice.