With the current bonus offer (through the end of January) you can buy 72,500 AA miles for $1450 plus taxes and a $30 fee, so call it $1600 or a bit less. AA charges 65K miles for business one way on its own metal or 70K on Oneworld partner metal.

You'd need to phone AA to see space on CX metal as they don't show it on their website. Or join AsiaMiles and look for space there before phoning AA to book.