Bed.
I think a ceasefire is a very real and possible thing; Murasa and Aya may be relatively unharmed, but they both have duties to their respective crews, who are in the process of completely mauling each other. If/when we do secure a temporary truce, however tense it may be, that's when I'd want to ask Aya directly if she's looking for the Mouthful Blade. Specifically namedropping it in her presence is important if it is indeed what she's looking for, because it gives us credibility (as opposed to asking her what she's looking for and then going "yeah, that's our thing", which could very well be a lie on our part for all she knows).