Op,

Being clueless as to when you actually want to take this trip (other than Fall), I did a cursory check on BA and there happened to be very reasonable availability via DOH on Qatar. Business class was available, and I believe it's just one award with AA miles. Not absolutely certain, but I think it's 75,000 miles one way, so you would need to top off your AA account with some SPG points.

As for the return, you could transfer some UR points to UA. Coach is readily available in October, with some days having business as well.