I'd think carefully about an AONEx as A seems a threatened species on many carriers. D is a certainty.
LHR-LAX will be on BA. Can you earn AA points on this sector?
DFW-ANC is summer seasonal (forget about winter). Even in AA F on the 757, this is not a pleasant experience for 7 hrs.
JFK-HKG will be on CX. Even on the AA code-share, can you use AA points to upgrade if you choose L class? I don't know whether you can use AA points to upgrade on CX.
Much of your routing has no A class so stick to D. If you use AA across the ocean you can upgrade to F that way, although we wont get into the debate on whether AA F is better than CX J...
LHR-LAX can be done on AA metal.
DFW-ANC as above, but same applies in terms of discomfort to LAX-SJU, in fact that one's a little longer.
JFK-HKG cannot be upgraded with AA miles.
As an AAdvantage member try to get the codeshares when you can, as this will get you your double redeemable miles as an EXP. Note that BA and JL don't give you any elite bonus for AA. And as you know, no AA credit for BA from LHR to anywhere in the USA (Canada, Caribbean OK).
Also of very important note: BA flights booked in L earn 25% EQM. L doesn't show as an earning class on CX at all. 70% on JL. So D may be the only way to get your full miles. Note that codeshares with an AA flight would earn full EQM and Double RDM.