Lord Raa said:
What chain of events takes Shinji from his insecure, slightly apathetic canon self to the point where he's in charge of NERV?
Shortly after Yui got sucked into the Evangelion, the Instrumentality Committee (with or without Gendo's knowledge) did their own occult experiments on Shinji, implanting Adam and otherwise fiddling with his AT field.
Since Adam wants to reunite with the Marshmallow Monster in NERV's basement, Adam gives Shinji instructions and prophetic visions about how to proceed toward Instrumentality.
Shinji thereby becomes the real "leader" of NERV, with Gendo as his public representative / political hatchet-man / Fuyutsuki style advisor. Unfortunately, he's still basically a scared, attention-deprived 14 year old kid. He just also happens to be the First Messenger's avatar-on-Earth as far as a bunch of creepy fanatics are concerned.