Apparently, the third time is a charm! I downloaded the firmware file again, rebooted my Mac, started the firmware update again, and this time it worked. Could there have been a problem with the first firmware download? The file unzipped okay and there was no indication that it was corrupt, so I don't really know why the update worked the third try but not the previous two. Perhaps my Origin was just being finicky.
At any rate, the update finally succeeded, the Jupiter patches are great, and I love my Origin!