Most of this is Asuka's perception of him. I wouldn't call someone who charges into a big red dildo thing with nothing but a knife and keeps going after said thing pierces his stomach a coward. While there IS some truth in the fact that he comes to her as a last resort (as well as in Asuka's claim that he just can't decide which chick he wants) I would say that his feelings are honest - which is the reason he gives for undoing instrumentality, btw. Also, he had the hots to her before everyone else sunk into depression or died.
Also, you can't blame a 14 year old for fantasizing about a hot chick in close proximity, expecially if said hot chick always keeps pushing her boobs into his face, but never lets him touch them. Of course, doing it next to her hospital bed is... very not good, but the "bad"/disgusting part is just that. If he'd gotten a room, he would've done nothing different from what lots of ppl of his age do regularily. In fact, one can asume that he was jerking off to Asuka, Misato and Rei all the time in his little room, we just didn't get to see it cuz it's not that interesting. The EoE bit is interesting because it's disturbing... because Asuka was right next to him. He didn't even uncover her on purpose.
You're certainly not implying he's a coward for not raping her, are you?
And for the "holding" part, maybe it would really help if Asuka didn't constantly act like she hates his guts.
He probably though he'd get a slap/kick in the face if he as much as touched her.
And if he'd had more of a "spine"?
Well, then he wouldn't have agreed to be used as experimentation material/for boredom in the first place.
He was still trying his best to be nice to her until episode 22... then she dissapeared off the map and wasn't found until she was comatose.