If you do the AA all-partner award to Indian Subcontinent (J is 135k), it stipulates transatlantic travel only, so that pretty much limits you to an AA/BA routing via LHR.
The best bet seems to be a oneworld award, where your required mileage is based on the actual miles you fly. See the sticky thread at the top of the forum or
this page at aa.com for more details.
A quick check of the mileage shows you could do the routing you proposed on AA/CX/BA, something like AUS-LAX-HKG-DAC-LHR-DFW-AUS, for under 20k flight miles, which would cost you only 130k for J, less actually than the Indian award above.
However, as flyupfront mentioned above, you're biggest problem now will be finding availability, so you might not have many choices.