Afaik there were no demos for the 2004 albums. They didn't like how they kept going back to those during SCWP. Solo guitar+voice recordings from songwriting might exist though.
Curtains was the only 2004 album that John recorded at home. The recording process lasted longer than for the other ones. So this could be previously unreleased songs from that session, or alternate takes.
Don't forget, the Mars Volta Wiltern shows happened during the recording of this album and Omar was around, playing on it.