If I understand correctly, the square notes (which I tried my best to duplicate in my notation) are chanting tones, but I played them just as regular whole notes.
Because this is a longer tune, I split the notation roughly in half. It was still a bit crowded, so I didn't put an "alternate notes" label for the alternate notes. The small lines above and below the staff at the end of the third line indicate where two sections of alternate notes abut.