All right, now that the dust has settled a bit and the community has had some time to investigate thoroughly, the closest thing that we have to 100% confirmation right now is that all of the "unknown" navigators from my original question can be earned from Score Attack. (There are scattered reports of other methods, such as mike's answermike's answer, but none that have been verifiably proven to work consistently that I'm aware of.)
Therefore, the closest thing I know of to an authoritative list at the moment is as such:
Teddie: Clear Story Mode completely
Mitsuru: Complete 100% of one character's challenges
Nanako: Beat Score Attack mode with Yu, Elizabeth, Naoto, and Shadow Labrys
Aigis: Beat Score Attack mode with Aigis, Labrys, and Mitsuru
Fuuka: Beat Score Attack mode with Yukiko, Akihiko, and Kanji
Yosuke: Beat Score Attack mode with Yosuke, Chie, and Teddie
For those who are absolutely dead-set to earn these unlocks by hand without resorting to spending money (or who wish to earn the achievements associated with them), note that you can slowly lame out a win against the AI via liberal application of the pause button. (Simply pause the game to see what move the opponent is performing, react appropriately, then repeat.)
I'll edit this answer if Atlus ever releases official unlock details.
