This is exactly what I was thinking while I was reading the post. It's a great plan, and I think it's the direction we need to take, but it's probably still not a philosophy we're going to be able to convince her of by the end of this conversation.
It's not supposed to cut it - I don't think anything is going to clearly get through to her immediately. The point isn't to logically convince her that she's a good person, because that's not how emotions work. The point is to set up/continue an extended campaign of affirmation. No matter how soundly argued, we're not going to get out of this conversation with her really, truly believing she isn't a terrible person. We probably won't even get her to say she's not a bad person out loud regardless of her belief. But we can establish and repeatedly emphasize that we don't think she's bad, that other people don't think she's bad, and that at the very least she can, ah, believe in the friends who believe in her, I guess. The emotional part of our brains are kind of dumb: repeat something enough and it will start to believe it. That's the part of the brain that we're targeting for the talk about why she does deserve to be happy.
On that note, I kind of want to approach that part of the conversation the same way you would in therapy. Of course, that's kind of hard since I'm not actually a therapist, but I know there are a few approaches we might use. The constant repetition that she isn't evil and we (that is, us and all of her other friends) do actually like her is one that we've already talked about. We might ask Mami and Madoka especially to make a point of complimenting her and asking for her opinion when it's relevant? Regardless, that's kind of by definition a long term thing, here it just means categorically denying that she doesn't deserve to be happy.
Let's see, I think it's also a thing to respond in the third person here. That is, go with the "that's a really mean thing to say about one of my closest friends" kind of line. I'm not sure if that will be helpful here, although it might be useful in surprising/confusing her and getting her attention away from self-loathing for a moment. I know it's a thing to get people to make a self-affirming statement even if they don't believe it. So, like, asking her to say "I am not a bad person," or "I deserve to be happy," as a way of kind of tricking the emotional parts of her brain to internalize it a little bit. Again, nothing that will get her to flat-out believe all this immediately, but things that will lead that way gradually with repetition.
So uh,
@Onmur and
@Kaizuki if any of those suggestions look good? I really think we need to approach this, at least in part, from the "this is a traumatized teenager, trying to reason them out of emotions is never going to work" angle, in addition to the more rational approach to try and change the underlying philosophy.