I think special weather statements are not treated the same as watches, warnings and advisories and not listed on
https://alerts.weather.gov, which is where this block is gathering its information. To pull this information would require some scraping of the local NWS page and seeing that each NWS is setup differently it would probably require some custom scripting to get this to show up.
Don't get me wrong, I would like to have this on my page too. I just know it would be a challenge to do.