One thing I know about Feist is that her method of songwriting for her most popular album was to carry a tape recorder to jot down bits and pieces that she assembled into songs later. If you listen carefully to her music, which is a bit collage-like and tends to present brief musical motifs with a lot of space between them, that explanation of her approach to composition makes sense.

It's not a style of songwriting I would associate with IEI, which I'd expect to be more stream of consciousness or focused on the whole concept from the start. There's also no strong overt emotion in Feist's music--the emotion is there, and sometimes she expresses with her voice an edgy pain, but that edginess is also somewhat created because of the way her vocals are recorded and processed, to add edge and grit to them (won't get into details here, but I've read about that, too). I could see her way of conveying emotion--where she's drawing you in and implying an emotional world rather than projecting it right into your face openly--as Fi, maybe.

She's very into visual impact in a way I associate with Se. Her father is an artist, IIRC correctly, and his influence seems to figure heavily into her aesthetic. I think I remember her discussing him in an interview.

There's nothing confessional about her work. She's not a wallower; she's a bit tough from my POV. She's pretty well in control of, even focused on, the technical aspects of her music. I think that's a big part of her sound and her success.

So I could see ESI for her. Can't see Beta anything, and she seems too intense for Alpha.