DFW-ANC is seasonal service running early May through mid September. FWIW, I'll be on the June 11 DFW-ANC flight.

While I was suggesting you purchase a separate HKG-HKT ticket, which would earn miles; KA, Dragon Air, flights are allowed on all oneworld products including ONE and CIR fares as noted below from the Technical Rules Sheet:
IME, A Class is only really important for the long haul flights including TPAC, TATL, Asia-Euro, and Euro-ME, and those are pretty much the only flights for which A class is always available (on your AONEx). Yes, you will find the arbitrary route on some shorter segments like BKK-HKG, ICN-HKG, and/or HKG/NRT. Now if Africa is included in an AONE4+ then SWP/Euro-Africa are also flights where F is nice. Now I will qualify this comment on the fact that I am 6'3"/190cm and 260lbs/120kg and a first class bed that is 78"+ pitch and 21"+ wide (36" on CX) is a huge plus IMO. Hence the reason I suggested your switch to CX HKG-LHR if you choose an AONE3. Food is much better too.