Ami's Faction
Founder: Ami
President: Ami's high Deceit skill
Treasurer: Mr. Wiggles the Piggy Bank
Members: N/A
Bwahahahaha!
I've had my suspicions that this is a possibility too. The strongest argument against it that I can think of is that Ren probably wouldn't be taken in by clever deceptions if Ami couldn't actually furnish anyone important supporting her.
-By related topics I mean out-of-the-blue questions that are none the less fitting given current thread of conversation.
Stuff like Uplift ideals => what's your clan patriarch's opinion on it? how about the rest of the clan?
All it takes is for her to ask the wrong question at the right time and note the flinch of pause in conversation too see that there's something that Hazou's hiding.
Sure, there are spies and they know the basics at least. Doesn't mean that additional source of info to cross-reference won't be useful for them.
-By inference I mean the terryfying power of Mori's mind. You give her a lead, she's gonna follow it.
For every subtle hint you give her, she'd get five probable answers and three further leads to pursue.
Mari's condition could be linked to Hana's resending back to Mist, and further show a general psychological vulnerability of the clan- easier to pressure their individual members, if not Jiraiya himself.
There are ways to handle that stuff. Shrug and say Hazou doesn't know and that Jiraiya is deeply inscrutable. Or tell her something plainly absurd, like that Hazou doesn't know because Jiraiya gets all of his advice from a very wise stuffed kitten that Keiko gave him and the kitten never saw fit to tell Hazou anything. That'd be hilarious.
Or more seriously, a perfectly valid approach is to tell the damn truth; 'Perhaps we could discuss that later, but I'm trying to get a feel for what you want without giving you any ammunition right now.' That's a respectable answer that shows he respects Ami's competence. It's important to never lie unless you've first asked yourself 'does telling the truth here actually seriously hurt me no matter how I do it?' and found the answer to be yes.
I think I'll add some suggested ways to deal with questions we're not comfortable answering to the plan I put together.
As for inferences Ami could make from non-answers, they may not be as helpful as you're thinking. Like, telling the absurd kitten story says 'He's obviously lying and doesn't want me to know so he's yanking my chain', but...what does that get Ami, really? It tells her Hazou doesn't want to give her detailed knowledge she can use for planning, but of course Hazou doesn't want to do that. He's not an actual idiot. He'd need to talk about stuff he has no reason to talk about to give Ami inferential connections to the Really Bad Topics I highlighted earlier.
Avoiding politics is just the absolute bare minimum policy. For all we know an offhand comment on Kagome's cooking will be enough for her to finish putting together that he's from a lost Whirlpool exclave hiding in the drained remains of the primordial sea beneath the Schezwan plateau.
This whole meeting is a bad idea, but we can at least try to steer away from the most apparent failure modes.
Ohhhh, that's why you're being so over-dramatic, you don't like the plan and want to support the closest version to not doing it at all that you can get.
The whole point of this exercise is to find out about Ami's political goals. Not talking about politics isn't gonna make that happen. Like it or not, we've gotta ask Ami about her politics or this whole exercise is a pointless waste of time. Rest assured that your estimation of the actual risks here is grossly overinflated. Asking 'So what do you want in the current political situation?' isn't going to trigger the apocalypse. It's safe to take off the drama queen hat.
Sanitized stories of our missing-nin adventures.
I'm actually somewhat worried that sanitized stories are the sort of talking around a missing truth situation that gives rich ground for Mori inference drawing. Maybe another safer topic? Or just stick with uplift and unusual training techniques.