My recommendation would be to fly eastbound on AA to LHR and then connect to EY for several reasons:

1) I believe CX still operates a regionally-configured A333 on HKG-BKK-KHI. Not a particularly pleasant hard product for a 9+ hour flight, including the stop. Even if it's being sold as long-haul J, CX is known to swap in a regional aircraft at the last minute on these [not so] regional flights.
2) You'll be able to fly in a premium cabin all the way to KHI with one less segment and quite a bit less travel time.
3) In my opinion, the premium (J/F) awards from Europe to India/Middle East represent some of the best values in AA mileage redemption - especially with EY as a redemption partner.

My recommended routing would be AUS-DFW-LHR-AUH-KHI on a combination of AA and EY.

-FlyerBeek