Yes, out of the creepy probably-haunted abandoned shrine is a good idea.

"I'm not going to have much time outside of working with Sasuke on his technique."

"Chihiro can help me, and I can probably work on my own on it a lot? The clones're good for that..."

"I'll see what I can come up with."

"Thanks, sensei."

And home. It's not ridiculously late, so he visits Hinata again, then stays up bouncing at Sasuke about plans for the fights.

Naruto throws himself fully into training the next day.

They have a visitor midway through the morning. Jiraiya is whistling as he approaches, but trails off when he sees all the clones Naruto has produced.

One of them stops what he's doing very briefly to wave hi, and then goes back to terrorizing the trees.

Jiraiya shakes his head, then continues over to where Kakashi and Sugira are doing speed training. "Talented kid you've got there," he says. "I don't think I've seen so many clones in one place before."

"He does it all on his own," Kakashi responds.

Great. Conversations with subtext. Sugira's barely good at overt statements.

He continues training, though he keeps an ear out.

     "Really?" Jiraiya strokes his chin. "Would you mind if I borrowed him for a while?"

"You'd have to ask him."

     "I'll do that, then. After I finish cleaning up that scribble you call a ward you left on this poor boy." He beckons Sugira over.

Sugira scowls, stops what he's doing, and walks over.

"Why the long face?"

Shrug. "Did you finish the analysis?"

"I did. That's why I'm here."

Nod. "For the ward, and to answer my questions?"

"Yes. So if you don't mind taking a little break, we can begin."

He nods. He was, fortunately, at a stopping point. And then Kakashi can use the time to help Naruto.

Jiraiya gets out his ink and brush and begins working.

"So. You had questions about Sages and natural chakra. Natural chakra is ambient to the environment, wild and untamed, unlike what your own chakra coils produce. A Sage is someone who can sense and use this chakra to power their own techniques. This is rare because natural chakra does not like being used, and if you can't control it, it will turn you to stone. That is not a metaphor, at Mount Myoboku the toads have a garden full of statues that were once those who sought to master the path of the Sage."

He has questions about the technical differences - what properties of natural chakra cause it to turn people to stone? Has anyone ever done a study on natural chakra? Also can anyone tell how thorough the transformation into stone is - does the person's soul stay attached, for instance? (He is aware a stone to flesh spell is possible and is morbidly curious what'll happen if he casts that on a statue-person.)

Natural chakra is not well studied at all. Most people aren't even aware it exists. The statues are, as far as anyone can tell, just statues now.

Hmmmmmm (that sounds like something to do science to when he finishes his five thousand other projects).

How is the seal interacting with nature chakra then?

It acts like a sieve, straining it out and storing it up. Acting like a miniature Sage, in other words. The part where it interfaces with his emotions is tied to this, somehow, and both are part of the seal at a very deep level.

Is it entangled in his emotional processing at all? Basically, is 'damages emotional processing' a failure mode of attempting to remove it?

...Potentially. Although if that happens it will likely rip out his chakra coils as well, in which case he'll have bigger problems.

That sounds like it, yes.

How entangled is it with different levels of 'him' - his body, his brain, his chakra, his soul?

(Honestly if his soul's fine he's not very worried, arcana can handle brains and bodies gracefully and doesn't so far have much trouble with chakra.)

Body and chakra most, naturally. Less so with the brain, but still some. As for the soul... Jiraiya won't speculate.