I would be surprised if your seven-year old would be permitted to fly solo in the economy cabin. One of the adults will need to fly there with the other child-minding in business class. One business award and two economy awards would likely work. If asked nicely CX might allow a one-time switch of adults half way through the flight. Or each adult flies business one direction.

You might also consider YVR and SFO for the long haul departures. Note that AA has improved the J seats, so if you can get/qualify for MCE seats on AA it might be more comfortable in the long haul.

Happy wandering

Fred