Okay, this sounds great. If this fanfic existed as described, I would read it.
Someone please write this...
That said, in regard to Kaworu, I imagine he'd turn up, as noted, of his own volition, intent on causing 3rd Impact, but grows attached to Rei and maybe tries to resist his call. Or, heck, maybe he fails to and begs l Rei to end his life, only for Rei to find a way to contain him instead.
Also, perhaps Rei is there at the start of the story, as per canon, and everyone knows where she came from. The reveal to readers that Yui popped her out of the core only comes mid-way through when Shinji tells the story to Asuka.
Also, thinking about Gendo. I imagine he's still somewhat cold, but is far less callous or manipulative or most of the other traits that made his canon self such a bastard. He's still like this occasionally, but only when he really needs to be and only to people he doesn't like. Meanwhile, I feel like with an understanding of what Yui was doing, he would be a better father to Shinji (and later Rei), but perhaps still the type to put his job first because of the importance of it.
That said, I imagine he still sends Shinji away, though not immediately, this time for his protection at Yui's last request, because the Secret Dead Sea Scrolls are a bitch to translate without SEELE's resources and they haven't been able to work out exactly when Sachiel will rock up to start things. Gendo makes a point of visiting his son almost literally every time he has a day off, and only calls him back to Tokyo-3 when he realises there's no other way to get Unit-01 to move, and that Yui probably knew this and just wanted her son to have as much of a normal childhood as possible.
As a bonus, on the day Sachiel appears, I can imagine this Gendo being in the comand center and giving Misato's crew a sort of speech along the lines of: "Fourteen years ago... We attempted to deal in powers not meant for us. We were foolish, arrogant, and the world paid the price. Today, we begin to rectify that error."
One final thing for this. Since NERV have direct access to the Secret Dead Sea Scrolls, rather than SEELE existing and keeping them under lock and key, they're able to consult them constantly. Because of this, they're treated as less of a religious text and more like the user guide they actually are. It takes a long time to decode them, and NERV, presumably Ritsuko or Naoko specifically, is still doing it when the Angel attacks begin, working out sections as the story progresses and new intel cones to light. They actually end up understanding the Scrolls far better than literally anyone did in canon, and learn a horrifying truth from them later on. The angels initially predicted up to Tabris are not the only ones, and they'll actually keep awakening and attacking almost indefinitely, getting more dangerous as time goes on (aka, the Pacific Rim Kaiju strategy). This also infers that, in canon in relation to this fic, the point in proceedings that the MP Evas attacked at wasn't selected because all of the Angels were dead, but because that was the end of the
first wave, a small lull where there was no chance of any Angels being active to interfere being the ideal moment for SEELE to carry out their plan.
It's entirely possible I let my imagination go a little crazy at the end there.
