By the way, does anyone have any comments on my vote? Because it's been almost two pages of votes and no-one has said anything... (no Echo you don't count you're the QM)
It lacks anything resembling Yui introducing the others to one another properly. In this update we have Maiko showing off that she knows Yumi's name already and Yumi staring at her until going pale when she (presumably) realizes who Maiko is, then conversation just marches forward. Somehow that doesn't seem like starting off on the right foot.
Therefore, Yui must take steps to ensure that the two of them become friends. Convince them that they'll get along, get Yumi to share mysterious legends that she's heard about Maiko and put a humorous spin on them to take the sting out, generally act immature to prompt the two of them into becoming exasperated in the exact same way which she can then point out to establish common ground between them, whatever.
Basically, this is a social engagement where two people are meeting for the first time, and we want that to go well- we can't afford to leave either party feeling neglected. Sending Yumi off on her own to make tea while we focus entirely on Maiko does not seem an optimal route toward making Yumi feel comfortable, and making her feel comfortable is likely to go a long way toward a successful recruitment pitch. Our highest priority needs to be acting as a good host, as it were, and only after that can we focus on either business (basement, corpses, dog, etc.) or address individual concerns (and both Maiko and Yumi clearly have them).
Calling in Minami seems like a good play, though. She's a bit quirky but Yumi's dealt with a lot of quirky people, and she's competent enough to give a good impression and interesting enough to hold a conversation with Yumi to keep her occupied while we slink off with Maiko to the basement- neatly avoids the issue of leaving Yumi alone to contemplate just how bad the situation we're trying to get her to sign up for might be/could get, what with the dozens of pictures of dead girls being a rather grim reminder of Momoko's legacy.