I can sort of explain Gendo's scheme near the end of 3.33.
So there's two different kinds of impacts - the one that is caused by an angel fusing with Lilith, called the Destructive Impact, and another caused by causing Rei+Embryonic Adam to merge with Lilith, called Constructive Impact that can only be done after ALL the angels have been killed. Neither SEELE nor Gendo want Destructive, but there's slight differences in the their Constructive Impacts. Gendo wants to kill God (also in manga) because he feels that God stole his only happiness, Yui, so in revenge he wants to kill God and take the throne and in the process resurrect Yui's soul that was not in Rei. SEELE, however, just want all human beings to become one and complement each other and push human evolution. That's why in EoE, SEELE's scenario happened instead of Gendo's - Rei didn't merge with Gendo and take him to see Yui, but went only herself.
Now for 3.33, the giant head in the headquarters is not of Yui's but of Giant Naked Rei (GNR) (that's why the head blows up when Lilith's other body blows up) and all the infinities have a modified face (just like in EoE, when the main GNR's face changed, the face of the Eva series also changed). Rei II and Yui are still in Eva 01, but another clone of Rei that was created by Gendo in the past 14 years had merged with Lilith. As for Eva Mark 06, which was supposed to be autonomous, since it's the 12th angel (seed of Adam), it had awakened and merged with Lilith body + (Rei with Lilith's soul) to create SEELE's scenario for Third Impact.
However, this is where I think Kaworu's explanations might be wrong because he completely misunderstands what caused the Third impact - he thought that Lilith had died and I think that's because he had thought both the spears were used to kill Lilith when 3rd Impact happened. But in actuality, both of them were the same spear and since apparently you need both types to fully stop the impact (remember that Asuka asks Shinji whether he wants the Third Impact to continue again), the last impact was just "paused" not stopped. What I imagine happened is that one spear was used by Mark 06 during the ritual (like in EoE, the Lance was needed by the Eva Series to start the complementation and it stabbed itself in the core), and then someone stopped it with the second spear by impaling Lilith's body. If it had fully completed, then it would be in the crucifixion pose not in the self-stabbing pose. Then, when Shinji took them both out, it got unpaused, and Rei 09 immediately released the angel by beheading it and then Eva 13 eats it (getting the fruit of life, like Eva 01 did in the series and thus it has been both awakened and also has the S2 engine so it can now become the Tree of Life like in EoE or in Rebuild, an Adam). Now, there's only one more angel to kill (Kaworu) and Gendo anticipated that this would again be a Near Fourth Impact. That's why Mari says "I wonder whether a demon or God will appear after the final Angel is killed." and also after seeing that one of the pilots is the "13th Angel that shouldn't have existed", she says "That's Gendo's aim huh?". After killing Kaworu, with the awakened Eva 13, he would be able to start his version of the Constructive Impact.
One thing that's offtopic is the observation that when Kaworu says he'll close the door of Guf, he wasn't the one that was stabbing the Eva. That stabbing is NEEDED for Fourth Impact, so the door only partially closes when he dies, not when he impales himself with the two spears. At least one of the spears is needed for the Impact.
