Hm. However:
1) Gendo didn't appear at work at all for one week after Yui's disappearance
2) When he did reappear, he had his Scenario ready
3) We know Rei is an - no, the integral part of the Scenario.
That's the A&T background (Gendo disappears for a week, and comes back with his plan), but is it confirmed as series background, or is that still open?
Well, everyone seems to call the Rei clones the 'dummy plugs', and that even though they are already ten years old. So it's possible that was the first idea. However, the fact that Asuka was snatched up so quickly indicates to me that someone in NERV must have known how things work. And let's not forget Yui certainly knew what would happen during her CE. So knowledge at the time can't have been that bad...
Given that everyone but Fuyutuski considered what happened to Yui an accident (and Fuyutsuki only knew because Yui told him otherwise beforehand), she doesn't appear to have told anyone else what she knew would happen during the CE... probably because they would have tried to stop her if she had. So a lot of the particulars of what Yui had worked out necessarily "died" with her. It's possible that they tested Asuka for compatibility with Unit-02 after Kyoko's contact experiment on a hunch, and developed the plans about using the mother/child pair to control the EVAs as a result. (Another idea: NERV Berlin might have initially hoped that they would finish development of the Dummy Plug in time, and could use Asuka as a pattern for their own Dummy Plug rather than having her act directly as a child soldier. No evidence for this, but no proof against, either, I think.)
So... Unit-00 is
constructed successfully, but they can't figure out how to actually make it move. Unit-01, under construction, undergoes Yui's contact experiment. Yui is lost, and the salvage attempt fails; either as a direct result, or in the aftermath, Rei is created. All indications are that her unique nature will enable her to control the Evangelion, and she's designated First Child at some point, but it turns out they can't just replicate her outright because there's only one soul to animate her no matter how many copies they make of her body. Dummy Plug project begins, to create a fake soul for synchronization purposes based on Rei's brain scans.
Meanwhile, in Berlin, Unit-02 is completed. Kyoko analyzes the results of Yui's experiment and implements safety features for her own Contact Experiment. (Theory: Kyoko expected to be able to directly link with the core of the EVA even without a resident soul, and then develop a way to control the Evangelion through that. Perhaps she expected to become the pilot
herself? Or develop a system that would let
anyone pilot EVA?) Unfortunately, she doesn't understand as much as she thought, and while physical absorption is prevented, her soul is
ripped in half, driving her insane. Metaphysical biology theory crossed over with psychological theory indicates that Asuka
should be able to synchronize with her mother's soul in the EVA to control it. She's tested, and the theory is correct. As part of the only mother soul/child pair NERV has at the moment, Asuka is designated Second Child and begins training. Plans are made to control subsequent Evangelions in the same fashion, in the event the Dummy Plug program doesn't bear fruit in time.
Question: Did the first Rei die
before Asuka's selection as a pilot? It seems likely, since Naoko didn't know of Rei as a designated pilot, and Asuka was designated Second Child rather than First. This suggests that the first Rei's death and the division of Rei's soul happened before Kyoko's experiment. Possibly without anyone at Tokyo-3 passing the details on to Berlin.
Back in Tokyo-3, as best we can tell, the combination of Rei's unusual psychological state, the poor quality of Unit-00s core, and the unusual soul bond limited Rei's effectiveness in synching with Unit-00, and she evidently hasn't had any luck yet with Unit-01 either in the anime (Manga continuity being a bit different). The Dummy Plug program has also fallen behind. The last straw is Rei's injury in the Unit-00 berserker incident, leaving NERV with no viable pilot/Unit pair in Japan -- Rei's too beat-up to pilot reliably, and hasn't yet managed to synch with the only usable Unit anyway. With projections indicating the Third Angel's arrival is imminent, in desperation, Gendo falls back on the mother-child system NERV-Berlin demonstrated, has Shinji designated Third Child, and requests his presence in Tokyo-3...