Handle two edge cases identified with the playing indicator behavior:
1. When enqueing songs from another parent, the prior parent is still
indicates as "playing" when it kind-of isn't.
2. When playback is stopped, the parent is not reset, and thus will
still be indicated as "playing" after the song has disappeared. This
is rarer and should be resolved in other ways, but the solution to
1 also fixes this.
Resolves#380.
c2def19aee