I don't know anything about the BA program.

For the outbound portion with the stop in Japan, I think you have 2 choices with your AA miles.

All-Partner + Asia1-Asia2 = 25,000 + 20,000 per person for Coach.

All-Partner would get you from SLC-ORD-NRT on AA or JL for example and then Asia1-Asia2 would get you from NRT-MNL on JL.

The other option I can think of would be a Oneworld Award using AA miles. But SLC-ORD-NRT-MNL is over 9,000 miles flown, so would require 70,000 AAdvantage miles per person. But it allows you more stopovers. If you could get to DEN or RNO then start your trip, you could fly through LAX, reducing miles flown to under 9,000 and it would be 60,000 miles per person. (RNO-LAX-NRT-HKG-MNL for example). You have to use two non-AA carriers though so the US-NRT segment would have to be JL and then you'd have to connect in HKG to MNL on CX to qualify.

I'm sure someone here can think of something I'm missing, and also fill in the gaps on the BA options. Good luck!