IMO ANGEL'S SONG's lyric is talking about something like Guardian Angel so I guess Ayu's transformation into the werewolf and protecting the people there is guardian angel-like. I always though it like that
While walking proud talks about lies and surrounded by lies...that maybe represent by imitation beings, robots, a lie to life itself and the fake scenery. That life full of lies made Ayu escaped and becomes the black-haired Ayu. In the end Ayu found that she herself have also made lies (her robot), the potrait of 'I'll be my ideal self someday'.
Moments from lyric-wise, I see Ayu potraying the person who is described in the lyrics, the one whose heart is broken and such, dying for protection and warmth. So she was like teary-eyed and gloomy. I don't really know the whole kids and the wooden doll thing. The stained Ayu in feathers and black paint? maybe describing the 'offering my wings to your wounded back'. idk