Remember that if you choose to go with AA, you need to book at H/Y/B fare if you're going in Y, which would be a more expensive option.
I assume that MPC does not have this restriction on the fare codes for earning Asia Miles. I was also told by the customer service person at CX that I can only enter the FF number for the one account that I wanted to be credited (either AAdvantage or Asia Miles, but not both).