This looks to me like a good case for a OneWorld award, which is based on mileage. I'm not sure whether the OneWorld award lets you end in a city other than the one where you began, but that's an easily solved problem.

If you can end in Europe, then a routing of ATL-LAX-SYD-BKK-CDG is 19974 miles according to the great circle mapper, which costs 100,000 miles. For a routing of ATL-LAX-SYD-BKK-LHR-ATL, that's 24,264 miles and costs 120,000 miles.

There's information about OW awards in this forum's sticky and at the AA web site.