Good idea.
By the time EoE starts, Shinji's pretty much an emotional wreck. If he was in a bad state when the show started, then he's pretty much just a massive, ugly hulking sack of depression and self-pity by the end. When he goes to Asuka's room, I think he truly did plan on getting some kind of closure with her. However, why Asuka? He's too scared of confrontation with his father, and Misato frightens him after pretty much offering to have sex with him. Asuka is the easy way out. When she doesn't wake up and he accidentally pulls her clothing open, we all know what happens next. The opportunity was there, and he took it. Of course, he had the frame of mind to lock the door; I guess he didn't want anybody seeing what he was doing. The shame I have a hard time placing. Obviously he's ashamed of spanking the monkey over a teenaged girl, but there's more to it than that. If you want a psyche analysis, by masturbating over her he is infusing her with his libido and expecting some sort of reciprocation or retaliation. Instead, he doesn't get anything. Since he has nothing to replace his libido, he gets a minor destrudo, prompting his line, "I'm so fucked up." For a more practical reason, he's masturbating over her because that's what he feels like he needs to do, and by being there she is helping him. She's not his mother, she's not his guardian; these facts make it all the easier to use her as a release of sexual tension. What walked into Asuka's room was a massive bag of tension, hormones, and emotions called Shinji Ikari.
Wow, I really needed to get that out.

