I think it's also helpful to point out that many, many, many
people are attracted to troubled, brooding loners with dark pasts, so even given what's happened to Shinji, it should be super easy for you to get away with portraying him as being popular with the opposite sex.
IKR? Look at how popular Sosuke is!
The fact that Shinji's not at all a bad-looking young man should do him favors as well in that department. If you want to portray his difficulty with that situation, I would suggest simply having him turn down their advances because of his depression. But especially in fictionland, romantic attention from others is not something he should be lacking. He can even play musical instruments with a lot of skill. The kid ticks off virtually all of the boxes for "troubled but cute pretty boy."
I actually had something in plan to that regard. There are these people who don't know who he really
is. So some of them would be attracted to him at first. . . then Shinji would have the breakdown that makes people think twice about pursuing him.
In regard to the Columbine shooter thing, I also think it's important to remember that very few people can be nihilistic and depressed every minute of every day.
I understand that, I really, REALLY do! But very few people are guilty of literally ALMOST CAUSING HUMAN EXTINCTION. If I did that, I guarantee you I'd be nihilistic and depressed every minute of every day for the rest of my life.
In order to avoid making him excessively pessimistic and dangerously insane, a few simple moments of him relaxing and being at peace, if only for a short while by playing the piano, cooking, gardening with Kaji, or enjoying nature or stargazing (as he's shown to enjoy in 3.0) would go a long way in reminding us that he's still human. Shinji is extremely resilient. If we're going to root for him, there has to be something that makes him smile, even if it's fleeting, and he should be shown experiencing that every once in a while. It's impossible to identify with a protagonist who's completely devoid of hope.
The problem with that is. . . well it's hard for someone to NOT be nihilistically depressed or suicidal when pretty much everything new you see reminds you of how much you've messed up and how you'll never be forgiven.
Enjoying nature? "What nature? The Ecosystems f*cked and I'm to blame." Stargazing? "Y'know that big red stain in the sky, the fact the moon's been ripped from it's natural orbit? That's my fault. Everytime I look at it, I'm reminded of what I am." Piano? "Reminds me of the one who manipulated me into causing another impact, who died to save my life for some stupid reason I'll never know the answer to."
Great! Now I've pushed him over the threshold from whiny, to genuinely Emo!
Is it any wonder he gets a bad rep? Even in fanfic, it's hard to make him likeable without betraying the core of the character!
I mentioned it before, but I think Shinji would adopt a self destructive lifestyle after what he's been through. Seemingly abandoned by (almost) everyone who ever said they cared for him, living with the guilt every day and night terrors every night, knowing that no matter what he does that was good, kind or virtuous you'd never be able to undo the biggest most horrible thing you'd ever done? Nobody will ever forgive or care for you unconditionally ever again, so why not be selfish?
Remember that porn-addicted otaku in 'Me!Me!Me!' ? I imagine Shinji's life after 3.33 to be a slightly more serious version of that (maybe without the porn). Plenty of people who've gone through the grinder in terms of heartbreak/traumatic experiences do a lot of disgusting things to themselves trying to make the pain go away.
Shinji has a lot of good qualities, even for all his faults, and having those good qualities on display once in a while would also mitigate some people's suspicions and distrust of him. Younger children especially. Maybe he saves a kid from a burning building, or something. I'm partially joking, but you get the idea.
Again, I have something like that in mind. . . I talked with El Mariachi about this in PMs. So I don't want to spoil it here. If you want a general idea of that so you can give advice PM.
In broad strokes. Someone asks for Shinji's help, and Shinji asks why he should bother given how the world's never helped him. Then, either out of pity, or guilt he helps out anyway.