However answering your question of how to appeal to this demographic, i will say that, Marvel already did. How? Iron Man, Thor, Captain America, these films had a lead that caught the female audience's atention, and had a romance they liked.
I know this because by Captain America the theatre was full of girls, many staying until after the credits, something that didn't happen in Iron Man 2, and they were exited for Avengers, man, there's a reason why in the poll the female audience has Avengers ahead of The Dark Knight Rises in terms of the films they're the most exited about. Loki is also receiving a lot of love
So there you have it, Marvel has already reached the Twilight/Hunger Games demographic, not only with his movie leading to Avengers, but X-Men: First Class is gaining some recognition with them and The Amazing Spider-Man seems to be heading that direction too.
If they want to go even more the Twilight/Hunger Games road then Runaways movie may be the best road.