I suggest calling e-service.

Similar thing happened to me last year when I was trying to book a SYD-HKG-SIN return ticket,, also up to the stage where I can select my seat and input credit card details.

I called CX e-serivce centre, they confirmed that seats area available, but they need to check with system, later in the day, they rang me back and able to ticket it for me. But this requires showing the credit card at the local CX office or upon check-in for the first flight sector.