As far as I am aware, yes, AW lost it's official faction position, hence all systems/bases (Omicron 74).
Yes, you should patrol Theta, to fight the war with the Corsairs there.
About that order, you should drop first the Zoner affiliation. The Zoners are currently on neutral terms with Corsairs and vice versa (NPC Diplomacy).
I would suggest to link 74 to Eta, and roleplay as Outcasts/Hessians, trying to keep the Corsairs at bay, preventing them from building a base on the other side of the minefield, and destroy the Outcast presence in that system (Eta).
The best faction which suits your RP (AW vs TBH war) are the Hessians. As mercenaries, you can be hired by the other factions, Outcast allied. This way, you will keep your Mercenary story up, and get a fair cash out of it:)