Originally Posted by
aktchi
This is almost 19K miles, so would cost 100K miles in Economy or 130K in Business: IMO the latter is well worth the extra outlay.
Because you have 1K mile wiggle room left, you can, if you wish, add a couple destinations that happen to on the way: eg, Tokyo, Honolulu:
RDU-JFK-YYZ-LHR-CAI-AMM-DXB-HKG-NRT-HNL-LAX
The above itinerary is 19,998 miles according to Great Circle.

If AA's calculator does not agree with that but you still want to do these extra cities, you can skip YYZ and fly JFK-LHR on AA:
RDU-JFK-LHR-CAI-AMM-DXB-HKG-NRT-HNL-LAX
Good luck.
The caveat is, HKG-NRT, NRT-HNL, HNL-LAX - are all on regional business class seats - much less desirable than the HKG-LAX CX longhaul business seat. NRT-HNL is probably on JL's sub which largely caters to tourist. Finally, good luck in getting HNL-LAX business class inventory.
Unless OP wants to go to HNL as well, I would totally skip Hawaii but would keep the NRT in the itinerary.
The BA YYZ-LHR beats the AA JFK-LHR, in terms of both hard product and soft product, eventhough the BA lounge in YYZ is rather smallish.