Your plan votes for "Naoto take the lead", which means Naoto will be doing the discussion.
If you wanted Amu to try it, as you pointed out in your plan, it would probably require "using Manipulation + Empathy + Socialise to try and ask more guiding questions or leak information to get a greater response" and Amu has a Socialize score of 0.
I don't know if Naoto has the stats for it, but that's definitely not an approach Amu is geared towards taking. Ideally, our approach wouldn't need a dice roll at all - but if it did, I definitely wouldn't want to take one that uses bad stats and poor dice.
That assumes that Kana is questioning her own value as a person. If Nero's theory is right, it's not so much Kana's "self-worth" that is the problem, but her conflicting desires in wanting to do two sets of things that appear to be mutually exclusive:
Of course, even that's still only a theory.
The only thing we can really say with any amount of certainty about her motivations is that Kana really wants her big sister Yui back.
Which we know because that was the same emotional lever Asahi used to get her daughter involved in the experiments, as you mentioned.
Appealing to anything else would involve relying on guesswork regarding her motivations.
I'm working from this:
"I just want to go home," Kana whispered quietly, crying into her shirt. "I don't want to fight. I don't want to kill people like Riku anymore. I… don't want to have to save Yui. I don't want to have to be the good one. I just want to see my mom again." She looked up at Amu, her expression so full of pleading and self-hate and sorrow that Amu couldn't help but flinch back from it—wishing desperately that she could do something, anything, but not knowing how; not knowing what.
Some guess work, but I wouldn't say from this that Yui is the biggest lever.
The Shadow / rejected desires seem to be focused on just going back to how her life was before she took that elevator down.
Unless you mean on Murderous Kana, who presumably doesn't want the original back because that's not the Scavenger aligned desire.
Or rather, is supressing her desire for such, hence Shadow, and wants to murder that desire because she's guilty about it.
Shadows usually aren't solved by external factors (saving Yui), it's an internal rejection of the self that needs to be accepted/resolved.
Granting the desires that created the Shadow doesn't change the fact that she rejected the desires in the first place, it would just let her ignore them.
Which would work as a temporary solution, if we are aiming for such as a priority.
I don't see it as a conflict of desires. I see it as Kana thinking it's wrong to want what her shadow wants. If that's the case, and we offer her what her shadow wants without first getting her to accept that it's okay to want those things, it'll backfire.
^ this exactly. Much neater put, Quine.
The problem is, at least under Nero's theory, one of the things Kana's Shadow might want is to not have to bear responsibility for Small Yui.
We know she has some level of responsibility that involves doing something for Yui whenever she sleeps, I assume this is necessary to maintain her "upkeep", whatever the heck it involves.
Would you really want to suggest that it's OK for Kana to not maintain Small Yui or bear any responsibility for her?
Well, yes?
She's a kid, she
shouldn't be responsible for such, and not wanting to have that pressure is perfectly reasonable.
Resolving the Shadow means accepting the desires. She can still chose to do it, but without rejecting that she would rather not.
Again, it's not about the actions taken, it's about her accepting that this is part of her. That's how Shadows work. They don't need solutions, they need to be accepted as valid parts of your desires. You can work on fulfilling those desires, or decide on balance that you prefer other mutually exclusive things more, but they are still part of what makes you who you are.
EDIT: Considering that Shadows tend to have an rather extreme version of the host/sources desires (See Rise).
In this case, Amu can probably somewhat cover for Kana in terms of keeping Yui together.
Kana being able to take a break and leave Yui to Amu on occasion might be enough to let her relax and accept she needs/wants to take breaks.
Caretaker burnout, etc, seems to be in play here.