Issues with that LA service not being "visible" for booking apparently are different from BA's apparent regional-sales-restrictions for A seats. l tried to book AKL-SYD using Cathay res, and was waitlisted. Eventually I telephoned LAN res and the agent couldn't even pull up the flight on her screen. When I insisted that they actually flew an airplane through that airspace on a regular basis, and sold seats to people called "passengers", she eventually relented and asked a supervisor. But it took a full 30 minutes on the phone for her to find the flight and give us the A seats. No problem issuing the seats, once she knew how. So no wonder Cathay and BA computers can't do it.
(I never flew the hard-won segment - the FT people who know these things convinced me that Qantas D service on that segment was just as good, and would allow me to sleep in until a normal hour.)