I am increasingly of the opinion that TDW does not. in fact, have one singular primary HQ. They still may but we'll see. We know per the in-game knowledge base the Nostrum starports were abandoned due to the incident in Tau Ceti. Currently the following are confirmed Nostrum starports (otherwise known as thestations):
Ortiz Moreno City (Tau Ceti)
Black Mausoleum (Beta Hydri)
Polya Coliseum (Aymifa)
Hunziker Orbital (Aymifa)
PEW-1901 (Aditi)
Mars High (Sol)
M. Gorbachev (Sol)
Galileo (Ocellus - Sol)
Brooks Estate (Pi-Fang)
Irkutsk (Alioth)
Leonard Nimoy Station (LHS 3006)
Vonarburg Co-operative (Wyrd)
Trade Post (Delta Pavonis)
Kummer Acropolis (Laedla)
Fort Dixon (Vega)
Wicca Town (Gateway)
As best I can tell, the anarchists, theocrats, democracies, and cooperatives have been coordinating efforts. These are their regional headquarters. They are closely connected to major systems from Frontier, First Encounters, the political capitals, and Engineers. This list is suspected of being very incomplete. The Cult of Sol from "Tales from the Frontier" is very real and very dangerous.