That's actually very similar to something that happened in a dream I had a while back about how 3.0 + 1.0 could potentially end. The dream showed a bittersweet sort of ending, and the more I think about it the more I kind of hope something similar to what happened in my dream happens in the actual movie. I shared it a while back in the Dreams About Evangelion thread, but I guess I could share it here too for anyone who is curious to know what happened in it:
It picks up during what I can only assume is near the end what would be the movie's story. I'll do my best to describe what I can remember and try to piece it together, given that a lot of context is missing. The ending I saw wasn't completely happy or completely tragic, but more along the lines of bittersweet. It starts by showing the end of Final Impact after Shinji has rejected Human Instrumentality, and he's inside some sort of giant red core thing filled with a swirling vortex of souls, and it's floating in the sky beneath the Gates of Guf. Unit 01 and Unit 13 are there as well, floating at opposite sides of the core thing, so I assume they played some part in initiating Final Impact. The core thing is being pulled into the Gates of Guf along with all the Failures of Infinity that were created during Third Impact, and seeing as there's no way for him to get out of the core, Shinji simply resigns himself to his fate of being pulled along with them, satisfied that he at least saved the world by stopping Human Instrumentality.
Asuka then shows up and dives into the core with her EVA in an attempt to save Shinji and pull him out, the whole scenario exactly mirroring what Shinji did at the end of 2.0 to save Rei and pull her out of Zeruel. As she's diving deeper and deeper into the core, Asuka's EVA is ripped apart and destroyed, leaving her to continue on in human form, and as this happens the contamination from Bardiel begins to spread all over her body. Asuka fights through the pain, determined to rescue Shinji, and one of the souls in the vortex she sees is that of Gendo (I guess the vortex contains the souls of the deceased, so I guess Gendo died), and she tells Gendo "You're the whole reason he ended up like this in the first place!", referring to Gendo's treatment of Shinji being what led him to become the person that he was. She eventually manages to make her way to Shinji, whose body is completely white and is just sitting there, much like Rei was inside Zeruel, and she reaches her hand out to him and says "Take my hand idiot!" Surprised to see Asuka there, Shinji grabs her hand and she pulls him out of the core with her, Asuka hugging him the same way Shinji hugged Rei after he pulled her out of Zeruel. After exiting the core, the leftover bits of Bardiel inside Asuka are destroyed, causing massive injuries to her body, and she lands in a pool of LCL on the ground below with Shinji.
As the Gates of Guf are closing, the soul of Rei II takes over as the dominant soul of Unit 01 and ejects Yui from it, after which Unit 01, controlled by the soul of Rei II, and Unit 13, controlled by the soul of Kaworu, are sent into space. Yui, now back in her human body, lands in the pool of LCL below, and as this is happening Rei and Kaworu's voices speak to her, telling her she should return to the ones who love her most rather than continuing to live in a false reality. According to Rei and Kaworu, what Yui did by placing her soul inside Unit 01 was no different than what Shinji did when he caused Near Third Impact by trying to save Rei, their selfish actions hurting the people closest to them and leading to all the grief and suffering that followed. Yui realizes her sin and decides to forget about whatever plan she had for the EVAs, ready to instead just go back to being with those who care about her.
In the next scene Shinji wakes up and finds himself in a hospital room, where he is greeted by Rei Q and Mari, and remembering what happened he asks them where Asuka is. They lead him to another room in the hospital, where Asuka is in critical condition. The damage Asuka's body sustained is severe, and now she is slowly dying. Nothing can save her now, and hearing this Shinji rushes over to her side, distraught and asking her why she went to such lengths to save him if she knew this would happen to her. Shinji apologizes to her repeatedly, saying that it's all his fault why she ended up like this and that she should have just left him, because now it's like he's killed her a second time. Asuka then reaches out towards Shinji and puts her hand on his face in a gentle manner (much like she did after Shinji tried to strangle her on the beach in End of Evangelion) and says "You can't even figure that out? You really are an idiot Shinji." smiling at him as she says this. She tells Shinji that it was her choice to do it, and, and that she doesn't regret it and would do it again if she had to. In her final moments Asuka's usual tsundere personality fades away and she shows a much kinder and softer side to Shinji. As she is dying Asuka asks Shinji to stay by her side, and he does, holding her hand until she finally succumbs to her injuries.
After this Shinji finds himself outside in the courtyard of the hospital by himself, where he remembers Kaworu's final words to him, feeling the same pain after Asuka's death that he felt after Kaworu's. Shinji now finally realizes how stupid and selfish he has really been, and that there were people who cared about him all along, one of them even going so far as to risk their life in the same way he did for Rei just to save him, but now she's dead. Shinji then breaks down into tears and starts crying, resenting the fact that he is only now realizing this when it's already too late. Seeing Shinji on his knees just bawling his eyes out like that was so heartbreaking to watch. Off in the distance, Yui, who is wearing a hospital gown and standing on one of the balconies, recognizes Shinji (at this point Shinji does not know she is back yet), and she walks down to the hospital courtyard to see him.
What follows is a really beautiful and heartfelt moment where Yui just quietly approaches Shinji hugs him. Thinking that it's Rei Q at first, the look on Shinji's face turns to one of pure shock when looks up and he sees that it's his mother Yui hugging him, not sure if what he is seeing is real or if it's a dream. Shinji must have been feeling so many different conflicting emotions in that moment. It sucks that Asuka died, and right as she and Shinji were finally opening up to each other and realizing how much the other meant to them, but at least on the plus side Shinji is now reunited with his mother. Everything then cuts to black, and all you can hear is Yui saying what she said to Shinji in End of Evangelion: "Anywhere can be paradise as long as you have the will to live. After all, you are alive, so you will always have the chance to be happy. As long as the Sun, the Moon, and the Earth exist, everything will be all right."
It then cuts to the next scene and some text appears that says "six years later" and it shows Shinji and Rei Q, who are now both older (both looking to be about 18-20), sitting in the back of a car being driven by Yui. Humanity has started to rebuild after the events of Final Impact, and things have seemingly begun to return to the way they were before. Yui and Shinji have since reconnected with each other, and Rei Q has been living with them, Yui having adopted her as a second child. Shinji now views Rei Q as his sister and Rei Q views Shinji as her brother, and the two have formed a strong sibling bond with each other. Rei Q in turn refers to Yui as "mother" and calls herself Rei Ikari, reflecting the fact that she has become a part of their family. This Rei has begun to develop a unique personality of her own, one distinct from that of the original Rei II, though she still seems a bit socially awkward. Rei also still has Shinji's SDAT, and apparently she has developed a taste for heavy metal music, which I found both odd and hilarious at the same time. Yui then stops the cars at some college campus and Shinji and Rei both get out a few suitcases they have packed, this being their first day of college. Yui tells them that she knows their teacher personally and that they will be alright, and she kisses them both goodbye before leaving.
After Yui leaves, presumably to go to work (wherever that might be now) Shinji and Rei head to their first class of the day and sit down. They are joined by Mari, who sits down next to them and appears to have aged a few years just like they have (I guess the Curse of the Eva was lifted after Final Impact, which is why Shinji, Rei, and Mari are all able to age now) and instead of her usual pigtails she now has her hair down all the way. Shinji and Mari seem to be really good friends, having stayed in contact with each other after the events of Final Impact, and they begin discussing the various nerdy things they're interested in. Next, the teacher finally walks in, and it's revealed to be Fuyutsuki, so I guess he survived the events of Final Impact and has gone back to teaching. I wonder who else survived, since there seems to be no sign of Misato or Ritsuko or any of the other Nerv staff who were a part of Willie. Perhaps teaching the next generation is Fuyutsuki's way of redeeming himself? Fuyutsuki then sees Shinji, Rei, and Mari sitting there together in the classroom, and he's immediately reminded of the time he first saw Yui in his classroom. He smiles and thinks to himself "it seems the end and the beginning really are one and the same". Hopefully this means things will turn out differently for Shinji, Rei, and Mari than they did for Gendo and Yui, and Fuyutsuki won't have to witness history repeat itself.
After this there's a quick montage of some random slice of life stuff that happens in their lives during college. In one shot Shinji is seen visiting Asuka's grave and leaving flowers, in another he and Mari are at some karaoke place singing together on stage, in another Rei seems to have made friends with a group of eccentric girls at the college and shows them a pile of love letters she has received from various boys at the college, feeling flustered and not sure what to do. Next there's a scene of Yui and Rei bonding together while gardening, and Shinji shows up with Mari. Shinji appears to be blushing, which might be a sign that he and Mari have started dating and is nervous about introducing her to Yui. The final shot then pans away to space, showing Unit 01 and Unit 13 in orbit around the Earth, and above Unit 01 is a ghostly representation of Rei II, while above Unit 13 is a ghostly representation of Kaworu (they're not literally there, but metaphorically), and that's where the dream ended. It was pretty cool getting to see how Shinji's life turned out. Shinji has suffered so much, and I'm glad he was able to be happy again and live normal life after reuniting with his mother. I guess the main underlying message behind this ending is that despite what may happen "life will go on." In a weird way, that alternate slice of life future Shinji saw in Episode 26 sort of came true, but in an unexpected way, and Asuka dying really made the whole thing bittersweet. I actually wouldn't mind reading a slice of life manga about Shinji's life after the Rebuilds, just as long as it doesn't do something stupid like making it so that nobody remembers anything about Human Instrumentality or the EVAs like the ending of the manga did, because that would pretty much invalidate all the lessons they learned.