Uh--busy day right now, so I'll be back later. But, Megan, I think you're trying to over-complicate it. Joan uses pretty much standard major and minor chords, but she often adds passing tones or rhythmic ornamentation. A musicologist might come along and analyse one of her accompaniments, and at a couple of points say "Oh, that's a 9th chord." But I don't think she thinks of it that way.

And there is a cohesive system of accompanying modal songs (i.e., "What chords do I use to accommany a song in Dorian mode, since the regular minor subdominant is obviously wrong?"), but there are no "modal chords" as such.

Sorry I don't have more time right now, but I'll be back.

Don Firth