Earlier quoted context omitted.
From what I gather from this page it seems organisations need to be added by the community or organisation members. I know a few organisations that aren't on that list for my country like https://github.com/GouvernementFR , https://github.com/DISIC , https://github.com/ANSSI-FR and https://github.com/ansforge . No promises but I might make a PR tonight on the page you mentioned.
That would be great, scraping that site is the entrypoint of my data pipeline!
Querying wikidata may also be useful https://github.com/github/government.github.com/issues/877
Added: note about your project at https://github.com/github/government.github.com/issues/1167