So I don't know if you'd rather toss these two together when Jane does not think she's always been a magical girl, as she'll be infiltrating rather than investigating -- but I actually think this could be an interesting combo for the Jaunt? Jane is the Oracle of Constellations, which for her is largely tied to trying to explain the mysteries of the universe, and intuitively drawing the lines of knowledge between things -- something that could tie interestingly in with the truth-based powers, maybe?

....I'm not sure where to go with it -- maybe Jane deciding Naoto needs a mentor or something? -- but it could go somewhere.