I don't think that the Shiodome office handles ticketing at all (there's no indication of it anywhere online). Have you tried the US or other international number, the Osaka city, or Kansai airport numbers? Those probably are less busy than the main or Tokyo lines. If you are still near Narita airport then ticketing staff (not others) should be able to help if you are willing to wait in line.
Given the size of the typhoon and the fact that access to the airport was cut off I'm not that surprised that the phone hold times and airport lines are long , but unfortunately the Japanese attitude to that is just to suck it up and get in line with everyone else.