I think there is no doubt that what Shinji did was absolutely sickening and deplorable. And nobody would believe that more strongly than Shinji himself.
However, I do not think Shinji is a fundamentally bad person. He would not have done what he did at the start of the series, or even halfway through it. By this point, Shinji is quite utterly broken. And he isn't proud of himself for doing it in the slightest. Even whilst he's in the middle of the "act" you can tell by his voice that he is hating himself for what he's doing, but can't stop himself.
As I mentioned in my previous post, the...incident is partly a result of sexual repression, self-inflicted repression at that. At no point prior to this do we see Shinji engaging in any kind of even vaguely romantic activity. He never flirts, never tries to express interest in anybody, never seems to "relieve" himself, and seems to feel ashamed of himself for thinking any even vaguely sexual thoughts about anyone. Just look how embarrassed and ashamed he felt after accidentally fell on top of Rei whilst she was naked.
Such repression (probably imposed because he felt that if he was so repressed, people would think better of him) led to a desire for intimacy, and in turn perverse lust. Whilst Shinji is in general a genuinely nice boy, he does have a dark side to him, one that has been exacerbated by his experiences, the mental strain of piloting Unit 01 (for example, becoming so highly synced with Unit 01 when it is going berserk will probably have caused a huge amount of damage to his brain, as piloting an Eva whilst highly synced can cause mental contamination, no doubt leaving him with a potential for fits of violent rage) and to some degree by his attempts to conceal it.
We can see this dark side later in the film, in an event which technically speaking occurs before the hospital scene. Shinji is completely traumatized after the events with Kaworu, and is pleading Asuka for some kind of comfort. Asuka is then, to put it mildly, extremely cruel to Shinji. Shinji completely snaps, and his other side appears, the side of him that is extremely prone to anger and violence. He completely loses control of himself and tries to strangle Asuka (which is potentially the reason she's in hospital anyway). This is just one facet of the side of Shinji which has grown like a tumour inside him: the aggressive, violent, lustful, bestial side which he has fought for so long to keep in check, but has eventually overwhelmed him.
I don't think that Shinji was shaking Asuka to get a reaction because he wanted to get back at her. At this point I think he was so depressed and desperate for intimacy and tenderness that any kind of attention, even being shouted at, would be better than having to watch one of your few friends (if Asuka can be called that) lying in a coma, completely unresponsive. Likewise, I think that his...ahem...date with Rosie Palms was once again out of a craving for intimacy, albeit a craving that has been perverted and warped by Shinji's shattered mind.
It's also worth mentioning that at this point, he doesn't just hate what he's done. He absolutely detests himself. He has realized that not only can he not protect his friends from the Angels and other people, he can't even protect them from himself. Hate him as much as you like, because it doesn't come close to how much he hates himself.
Another point which I think is quite interesting is something related to Shinji's character from a writing standpoint, rather than why he did what he did in terms of the story. Shinji is actually a genderflip of the traditional useless moeblob female character. He is reclusive, vulnerable, prone to becoming very upset easily (although for good reason), has inner strength that they cannot realize, falls over a lot, longs for praise from someone they look up to (although it's his father instead of a boyfriend, and he doesn't exactly love him) and clings to what little affection he can get. Now imagine if Asuka was a boy, called Akira, and Shinji was a girl, called Seiko. Put them in the hospital scene. Now, a cute young girl masturbating by the side of the bed of a boy she feels affection for whilst he sleeps would be considered "cute" by many (and probably wouldn't be considered as sexual assault), even if it is still rather...odd. However, when the genders are reversed, it suddenly seems a lot less moe and a lot more creepy (let's be clear, it IS creepy). This could be a way of Anno looking at the rather stagnated traditions, putting a new spin on them, and making people realize how horrible said traditions actually are. Because according to Otaku:
Girl pleasures herself to thoughts of boy (or a girl for that matter)=cute.
Other way around=bleh.
Of course I'm not saying that we should say that "Aww, Shinji is so cute the way he faps next to Asuka!" (although I do think that EoE Shinji is a character who deserves at the very least pity) but rather that the idea of masturbating next to someone whilst they sleep is in no way cute, regardless of who is doing it to who.
Here lies Squigsquasher.