1) I think we have other indications that the JPs are not secretly backing Manticore
Like? It's not (just) us questers you need to convince, it's Kana and "It's not paranoia if they are really out to get you" Naomi here.
2) the relevant comparison is between us and the JPs, not between the JPs and Manticore
I was using "JPs are competent, Manticore aren't" as a basis for that conclusion (because if they were linked they would have shared), and Baughn pointed out the apparent difference might not be true, so...
Since we technically don't know what Kana is actually going to do...
[X] Plan Tricologe
-[X] Amu:
--[X] Make cake and chocolate milk, like we had with Kana the day we first met. Offer her some.
--[X] Ask for her side of the story. Listen to it.
--[X] Emphasize her self-worth, and the legitimacy of her feelings. (Not just the feelings she's suppressing, either.)
--[X] Tell Kana that it isn't wrong to want to not to have to fight or hurt people or save them or even be a good person. Tell her it also isn't wrong wanting to fight, hurt and save people. It's fine for someone to want both at once.
---[X] Show Kana telepathically the fight you had at Nikaidou's lab long ago. Amu, as Amulet Heart with Ran, wanted nothing more than to brain Nikaidou with a heavy rod for kidnapping her Charas. But Su wanted to help him instead, to heal and save him despite his sins. Despite differing mindsets, neither parts of Amu were "wrong".
--[X] Chara-change in turn with Ran and Su, displaying the proof that it is fine for someone to want to be 2 or even 3 or more different things at once: After all, you and Utau live it every day, and surely both of us are fine regardless?
--[X] Remind Kana you didn't give up on Utau, despite everything she did, and you won't give up on Kana either. So if Kana doesn't want to give up on her mother too despite everything, that's also fine. Whatever she decides, you'll help her; we don't mind talking to Naomi on your behalf if necessary.
--[X] Offer to help take care of Yui in the future if Kana would like to share some of her worries and troubles.
--[X] Inform Kana there may be a way to heal Yui, if she wants to try, but it will require Kana's willing help.
---[X] Show Kana how you retrieved your own fragments from the Road of Stars - Ran, Miki and Su - and offer to either lend her Dia's assistance or put her in touch with Tsukasa, who seems to have his own way of getting there, to try the same thing.
Pistachio's plan was missing a way to convert a fight into a conversation, and Quine's plan doesn't take advantage of Utau narratively being good with words, so I decided to merge the two and slightly modify? (Plan name is also a song title that may be relevant)
Might need to apply a calcinator to it though, it's a very long plan as-is.
Edit: Still long, but slightly shorter now