Well, I've figured out Extraordinary Machine. There are eight beats per line, but the lyrics don't quite fit the pattern and spill into the previous line. Also, sometimes there are no lyrics at all during the beat: they're syncopated in parts, which is how she gets away with putting so many syllables in some of the lines. For example:
(pause) I noticed that my opponent is always on the go, and
won't go slow so's not to focus, and I notice (pause) (pause) he'll
hitch a ride with any guide as long as they go back from whence he came, but he's
no good at being uncomfortable so he can't stop staying exactly the same.
The first, second, and last of those four lines all share a rhythm, but in the third line, only beats 1, 3, 5, and 7 take place when she's singing. I wonder if this song would be less perplexing to someone who's had some music theory classes and is trained to understand these things. It's just strange because it features so many things you don't hear in "normal" music, where words happen on the beats and everyone's happy.
Anyway, it's quite an intriguing song, and it sounds really good too. It's been stuck in my head for a while now.