Ima, Soko ni Iru Boku, Noein: Mou Hitori no Kimi e Recommendations
Both deal with a world that is dying and needs a girl to help them survive. Their plots are both very dark despite having some lighthearted moments.
Similar concept and setting. Touching and subtle; main characters are children who travel through time and witness a lot of destruction and grief.
Setting looks very familiar.
MacGuffin Girl, or maybe its just a girl wearing a MacGuffin -> said MacGuffin holds great powers a Bad Future is trying to get a hold of -> male friend trying to save her from said organization.
Time traveling + wars tearing countries/futures apart.
Although Noein is a lot more "positive" than NT, HT.