I really like this breakdown of Jason because I've never thought of him as an INTP. Me being an INTP myself, I thought Annabeth was closer than any other character. But she seems a little too xxxJ to me. But INTPs can be like INTJs on certain topics and projects. . . and the way she had to innovate quickly without getting too frustrated makes me wonder if INTJs can be like INTPs on occasion.
But I never considered Jason to be INTP before. I've always kinda thought of him as an ESxx, but whenever a character seems a little dumb or showy to me I automatically classify them as ESFP until I can narrow it down, so I clearly have some bias against that. Jason is a protagonist, but he also has some inferior Fe and prefers to do things quietly. . . the first example I can think of is the beginning of Jason's being a character, when he randomly wakes up and is holding hands with Piper on a bus. I can recall that he doesn't understand it but doesn't want to freak her out or hurt her feelings, which is a small component of what he thought in that moment. But he still doesn't really strike me as INTP; none of the characters in this series do for me except Annabeth and y'know. Jason seems a little more ISTJ-ey for me. But you definitely are right about his inferior Fe.
This would give us these Fe types (bold is Fe inferior):
INTP, ISTP, INFJ, ISFJ, ENFJ, ESFJ, ENTP, ESTP
From these, I'd say ISTP makes the MOST sense if it had to. Jason rather misses how things fit together, but he gets all the details down. In the end he decides to go his own way, stemming from his sense of duty. The work he would do is kind of alone work, but decides to do it for good reason. This would give him Ti-Se-Ni-Fe, which I think makes sense.
In the Lost Hero, Jason is seriously taking in every single external detail and trying to apply it to him. The descriptions of scenery and life through Jason's perspective leads me to think he does have some Se. He also has a lot of internalized connections about what he sees. Like he concludes, based on the way Coach Hedge was looking at him, Hedge knew Jason didn't belong there and Jason feared some kind of trouble that way.
Jason and Percy seemed to share some of the same views, but Jason is a bit more internal about it than Percy is. I've seen a lot of types for Percy on here, though, so I'm not sure what Percy would be based on Jason. If Jason is Ti, then I'd assume Percy to be inferior Te, like ISFP.
I think it's also fair to remember that a lot of these characters would not be the average person you type with MBTI. Trauma can cause the functions to get off-balance and change personality, like how everyone is noting that Nico was "Extroverted" before Bianca died. I believe he just lost some of the faith he had in people generally and started to keep it internal. He liked to care about people, but from far away and in his own head. INFP makes sense for Nico because the INFPs I've known were like that as children. Introverts can seem very extroverted at times and Nico always did stick around Bianca. So I'm not sure I would call his ten-year-old self ENFP. Also, I've heard that many psychologists and such refuse to use MBTI on kids younger than fourteen because it wouldn't be as accurate. So these are all things to put into account.
So that would mean we have
Jason ISTP
Annabeth INTJ
Percy ESFP-ish
Nico INFP
Now I'm having a hard time typing Bianca. Not only because she was only around for one book, but because she's kinda faint in my memory and I do believe her to be xNTP. I'm thinking this because she did leave Nico behind and showed little remorse for it, because the Hunters made more sense to her and Nico was sure to be taken care of. Nico was definitely hurt by this, but Bianca still didn't care all that much. She loved to debate and argue about her beliefs, is all I can really remember about her. I'm thinking ENTP because she seemed to mesh into the Hunters seamlessly. If she were INTP, she would just be standing there like "Um hey".
Jason ISTP
Annabeth INTJ
Percy ESFP-ish
Nico INFP
Bianca ENTP
I think it's difficult for me to remember, when typing these characters, some occasions you are directly in their head and sometimes you're on the outside. In introverts, which most of the 7 seem to be Introverted, your primary function isn't immediately noticeable unless you are directly living in their head.
Percy's perspective in the PJO books really help us out on this. At the very beginning of The Lightning Thief he has a monologue about who he is generally. He feels cheated and isolated. I'm not sure if he isn't social because he moves school so much and things don't make sense to him, or if he genuinely is introverted. But I do think of the way Percy meets new demigods and such. A lot of the other, more obviously introverted characters, are more nervous and obviously tense. And when he first arrives at Camp Half Blood he gets off the porch and decides to just walk around like "Hey how are you and how are you and how are you", more in his head than outside of it, but you probably get it.
Meanwhile, Jason wakes up somewhere he doesn't belong and he's like "AAAAH AAAAH AHHHH" everywhere he looks.
Again in Son of Neptune when Percy is running from the gorgons he reaches a point where he's like "This exist and that exists and this makes me feel this and this could be this y'know", which makes me think he could be a more introverted ESFP. I'm having a hard time understanding ESFPs because the stereotype is they're stupid party animals, but I'm thinking ESFPs just might not be the best for institution, which Percy definitely isn't. Leo isn't really either. So it might be an xSxP thing.
Here's my final delineations:
Percy ESFP
Jason ISTP
Nico INFP
Bianca ENTP
Annabeth INTJ
Leo ISTP
Other than that, I haven't really thought about it.