Is your BOGO from BA the 2-for-1 deal for spending $30K on the Chase BA Visa? If so, that is only eligible for use on BA flights. You'd have to fly through London.
I think UA/US would be best for you, since *A is big in both BKK (TG) and TYO (NH). Even UA runs a daily NRT-BKK flight. AA would require more miles due to their stopover rules.