I think I can narrow it down to Microcentrum californicum. I was reading the info on this page, and the link to the California Angle-wing's song is exactly the same sound that the insect in my photos was making. It helps that there is only one other Microcentrum species in the Bay Area to compare it to. Would it be possible to create a new species page for this insect?

Thanks! I was thinking it might have been the Mediterranean Katydid, but Microcentrum looks closer.