I fear that even if the "through" HNL - LHR segment were deemed an acceptable routing, that you might have a great deal of trouble finding "through" A inventory (there's nearly no "A" class inventory on any AA flight ex-Hawaii). Without a "through" A class seat, it will be very hard -- if not impossible -- to hide the HNL - LAX sector.

It would appear that you have very few sectors in F (A): DOH - SYD, HKG - JFK, JFK - LAX, and presumably LAX - LHR. Were you planning on more?