People have been consistently invoking our advanced insight but there is another relevant insight, namely:
"Though a path might be hard and lonely, it has worth if you can present something of beauty to those you care for at the end."
This insight has been one that LQ repeatedly has trouble with, as she takes a very selfish view of it. The idea that it also applies to her friends and family is anathema to her. That's very, very dangerous for her in the long term and she needs to recognize that her allies can take risks as well, potentially even to her own benefit. At the same time we do have a responsibility to keep Hanyi in particular safe, so she might not be a good person to explore that with.
Secondly, while the negotiations are indeed at risk here, it is not from the the position of our hosts. Rather, Ling Qi is viscerally upset by the Voice's request and Jaromila appears to me to be concerned that the Voice just singlehandedly destroyed the negotiations. Remember, we intentionally make our feelings on things extremely obvious. We have built our social toolkit around such radical honesty and transparency, though we can certainly hide things such as with the spiders. One of the better justifications for LQ speaking up immediately is to let them know that, while indeed mortally offended, LQ is not going to abandon the talks because of it. Letting Hanyi speak first is potentially leaving Jaromila to twist in the breeze for a little while.
Also Zhengui just shouted that he objects and I'm pretty sure they can hear him (especially the Voice), so even if we did hide our feelings it would still be obvious to everyone that this is a big deal. Letting them hear Hanyi's thoughts helps them more fully understand our position anyway, so might well be a better thing for the negotiations going forward despite the initial confusion.
"One half a year," the Voice said. "With oaths of good health and protection. Your line would be compensated."
"Huh no way!" Zhengui protested in her mind
Ling Qi blinked, startled into silence by the sudden demand. Hanyi looked just as surprised. Beside them she caught a brief frown on Jaromila's face before it was smoothed away.
Thirdly, if Hanyi truly goes off the rails, we have a technique that lets us pretty effortlessly interject and get things back on track. Giving her a frankly unreasonable amount of responsibility and freedom also makes a lot of sense for someone who, at Hanyi's mental age, had been living on the streets with her very life at stake on her decisions. We have also given Hanyi a great deal of freedom in the past, to the point where we didn't notice that she had been harassing a fellow disciple. This is perhaps not the healthiest way to parent Hanyi but giving her too much freedom isn't out of character for their relationship.
We've also been pushing Hanyi to develop her own identity, which expressing her own opinions would help with, so maybe it would actually be good for her to talk here.