I don't think the OP exactly included a rundown on all the intricacies of Personas.
As far as I know, they were a representation of the Inner psyche. In fact, the OP just says they're a representation of the psyche. There's no real logical reason to believe that that meant the outer psyche/fake you. It also gives very little info about the Arcanas, which is probably why Blitz chose the Sun. Unless you already knew quite a bit about the Persona games, or did a lot of research before making your character, going into this you can't really be blamed for lack of knowledge.
Plus, the wiki says, and I copypasta, "Shadows are malevolent manifestations of one's inner thoughts, while a Persona is a manifestation of the same feelings but tamed and trained.", in addition to "A Persona is a manifestation of a person's personality in the Persona series, referred to as a "mask" for an individual to use to face hardship."
While it says mask, it's talking about what you use to fight giant demon things, and, well...hardship takes on a different meaning.
"Through your Personas, your unspoken desires were manifested..."
—Metis
"A shadow is suppressed power, and when controlled by one's ego, it becomes a Persona..."
—unofficial project document, read by Naoto Shirogane
"Shadows are suppressed human thoughts given form… everybody has them inside."
—Teddie
"While Philemon describes the Personas as reflections of a character's inner self..."
"The Initial Persona (初期ペルソナ?) is the Persona that represents the most inner thought of its host."
...You can see why I was rather unconvinced of Personas being the outer/fake self.