I would put them into Continental. AA or BA might provide decent prices but they don't provide the same availability. Star just has way more flights and options. When it comes time to booking it will be all about availability as award seats to Asia are always very tough to come by. Star blows oneworld out of the water when it comes to availability.

I would choose CO over ANA due to the lack of fuel surcharges. I might choose AC over CO if booking before June 15 but not if I was going to book after since AC will be more expensive and offers no real advantage. CO will also begin offering one way awards.

Though honestly if your credit can handle it, do both AA and CO cards. Then you can transfer amex points as needed and you can probably even wait to transfer the points until you see what award availability looks like for the days you need.

You could even do CO one way and AA the other.