1) What class of service?
2) Your proposed route presents a few challenges.
a) BA only flies into IAD, but AA does not fly from IAD to NYC direct so you need to fly out of DCA which causes a surface segment or connect somewhere.
b) AA does not fly SEA-SFO on their own metal. They codeshare on AS but that isn't allowed on a xONEx.
c) AA does not fly from SFO-HNL direct any more so you need to connect in LAX or PHX or DFW.
I would look at something like: EDI-LHR-JFK-DCA-ORD-SEA/SFO-xDFW-HNL-NRT-HKG-PER-SYD-LHR-EDI and buy a cheap SEA-SFO ticket. If you are willing to change your US routing you could get a better usage out of the segments.