The Melancholy of Shinji Ikari
Background:
Kyon and Mikuru relationship had always put on hold due to Haruhi's jealousy. However, right after one of Haruhi's stunts where Mikuru is badly hurt both emotionally and physically, Haruhi sees Kyon tell Mikuru that he loves her. Haruhi disappears, and the Agency tracks her down to the north pole where the largest closed space ever appeared and was beginning to encompass the globe.
In desperation, The Agency brings Kyon to the North Pole, just in time to witness the appearance of a huge blue giant. Second Impact.
"Kyon, what's your real name anyway?"
"John Smith."
"We both know that isn't true."
"... Its Gendo. Ikari Gendo."
Plot:
Basically, the universe was spared when the Agency and the Time Travellers killed her. This didn't stop her, and she was split between her prersonality and her powers (the Agency is responsible for the all pseudo-christian motiff of the NGE series; Haruhi is god after all). With the world in such a horrible state, Seele/The Agency decided that the only way to progress forward was to coax Haruhi into creating a new one.
Haruhi's soul was reborn as Shinji Ikari, the son of Kyon and Mikuru (the baby was just written into reality -- Shinji shares the DNA of Kron and Mikuru, but Mikuru never conceived him). Seele, the IDE, and the time travellers create Nerv and Tokyo-3 as the new SOS. Maybe Haruhi really just wants to stay close to Kyon (and Mikuru, because despite her jealousy Mikuru is probably the closest friend Haruhi had next to Kyon) which is why she gets reborn as his son.. (This is why Gendo is cold towards shinji -- Seele wants a new, better earth, and making Shinji uncomfortable [but not to the point of just destroying the world]).
Later on, Haruhi's subconciousness will generate celestials/angels that try their best to reunite with Haruhi's power/Adam/Lilith. Nerv and Seele, wanting to control the situation, create the evangelions to prevent premature contact (shinji was made pilot because it made fighting the angels much easier when their creator wanted them dead). The IDE Send help in the form of Re/Yuki who was to pilot the Evangelions.
Unfortunately, Yui/Mikuru disappears during the activation of unit 1. This was largely suspected as a result (again) of Haruhi's jealousy. This results creating even more distance between Shinji and Gendo.
Dr. Ritsuko Akagi was killed by Rei for messing with Kyon and trying to hack into the IDE.
The story would likely end in the TV version, not the end of evangelion movie. Haruhi/Shinji rewrites reality into something altogether more pleasant.

