I don't think we can get the Pangolins on board, because a) this isn't Summoning, anyone we send could actually die which is a very different kind of agreement from what we have with our Tessera, and b) the Pangolins as a whole do not want to seek confrontation with the Crows, and I doubt we can convince them otherwise. We can ask them to send messages, though, and Jiraiya might find sending a message through that vector more poignant or something, so it's worth mentioning.
To be fair, they are single-handily conquering the world thank to us.
"The Crows summoner kidnapped our adopted brother" is kinda a big deal,as far as "Help needed" is concerned.
They can refuse, of course...that would be the equivalent of spitting in the face of their benefactor, to the point that Keiko could be completely justified in cutting the supply of skywalkers unless they are attacked.
So they would need to choice between potentially starting a war with a faction they want to conquer....or risking antagonizing the one that it's giving them such victories in the first place.
Refusing to help would imply that the Pangoling don't have our back in life or death business, after we gave them world domination...that's, a
big statement to make, so even if they refuse we can use it to our advantage in future negotiation, or to diminish the amount of seal we give them, under the pretense of betrayal.
"We gave you
everything we have, risking death to the other summoners, and this is how you repair us? We can't trust you with our full capabilities i see".
What can the Pangoling do to us? Cut off our resources? No more seals, this means they do that, they are all dead, the rest of the factions would crush them once they found out they are vulnerable.
In short, without Pangoling money we are fucked, but the without our seal the Pangoling are fucked, even worse than us, now that they overplayed their hands.
We are in a far stronger negotiation position with them than it seems, and we can(and should) ask Jiraiya about it when we have time
Yeah, I'd much rather just ask her if she intended this consequence. We don't need to be angry at her unless she intentionally jeopardized the Leaf-Mist alliance, and if it wasn't intentional then we don't need to sour relations with her for no reason. She's hopefully going to be a strong ally in the future, and I personally would be sad if Hazou formed a grudge against her if we can avoid it.
(For similar reasons I think the mic drop isn't a good idea. Beyond the question of whether we could get away before she responds, it also means we can't stay behind and, say, tell Jiraiya that we've got an idea or finish overseeing the end of events)
Personally i would be very careful in how we frame the question, Ami is not a omniscient monster, as much as she likes to give this impression, let's not give her the impression we believe she's more OP than she actually is.
Of course, my opinion is that we should completely re-frame our relationship with Ami and just enjoy the crazy: Hazou can't win against Ami if he sees everything she does as an attack, and not an enjoyable thing, because he will always be put on the defensive by the first crazy thing she does.
Narratively it makes sense: Hazou always behave in strange things, so knowing he doesn't need to control everything he does in fear of doing something crazy, because Ami is worse, would really help him, on top of that it would make Ami attacks far less useful, and it would give Hazou interest in seeing if Ami actually enjoy these things or not.