I think that the real story behind the EVAs story was the mental transition made by Shingi (the main character). As you can see in the begining of the series he was a very shy guy that never thought he could defeat his father. And at the end he is a more "violent" person more confident on himself. The real story is not about the evas, the angels an the end of the world. Is about the mentallity of our characters and how each one has changed because of the NERV corporation and the secound impact. The story is about the emotional and phycological transition the character has during the story. The end of the world is just something aside that is happening (like a side story to confuse you from the real story). That is way in the last two episodes are very strnge and in the last episode everybody starts clapping because Shingi is a better person (is like if he is trying to find himself and he finally did).
The movie was just to finish the side story (the end of the world story) for it not to be flying around without an end. They diceded to make the movie to give an answer to all the questions that didnt had an answer in the series. (In the EVA story). To understand the story you have to see it as 2 different stories:
1) What Shingi is passing thou and the mentallity change.
2) The EVA story and the end of the world.
This would make the explanation easier. You also see way Rei and Asuka are part of the experiments and way they decided to be part of them. Rei> Had no choice
Asuka> Wanted to be accepted by the others and be or feel special because her mother was crazy.
Shingi> Whats to proof to his dad he is worthy.
I hope this could answer your questions.

ATTE: EXODO
Studios:STUDIOS EXODO