Great review (quite accurate, although I'd give the score a half star more), but a few amendments should be made.
First, the creators of Laura actually have already worked with some Media Ventures composers, specifically Henning Lohner, who scored one of their previous films. Second thing is that I think Zimmer composed two themes, one is the lullaby and the second is very similar to The Thin Red Line's light and later was reworked for Spanglish actually, which might be pretty good evidence for Zimmer's writing of the theme.
Besides, very good review. And yes. Stay is a bit annoying .