I've been holding back on mentioning the book until we can at least exchange a few words first. If we offer it to her, and she accepts (under any conditions), she's under no obligation to do what she says, and we lose what may be our only bargaining chip. I can easily see her taking it, and not changing her tone towards either Iku or Tenshi. So I don't want to play it just yet. We may have a certain psychological advantage already, in that we have done what ought to be impossible, and potentially disarmed the ace that she's used to relying on when dealing with people.
I am a little concerned for Tenshi, admittedly, but I'm not sure the spectre has enough foresight to try to use her as leverage against us, and right now she seems to be mostly ignoring her. The thing is, we can get ourselves out, but not Tenshi. Maybe the spectre won't make that connection? Either way, if it looks like Tenshi is starting to get sucked in, we shoot her; no hesitation. Other acts of aggression on her part can be met with more moderate response.
Otherwise I don't suppose I have a plan, as such. Gauge her reaction, and try to move forward as seems best at the moment. I'm willing to extend at least a little faith towards her, regarding the book. I just didn't want to do it quite yet (unless you think we really should?)