Airlines routinely have promotions that only available on their own web sites. However, be careful. No matter where you book: If it is CX flight number, then no AA miles on K, M, L, V, Q, S, G, N booking classes; if AA flt number (even if operated by CX), then 100% miles.
What's the fare? If it is openly published fare (as you seem to imply), please post for all. If tricks or privileged info is involved, please PM me,

as I am a fellow ORD person very interested in ORD-HKG.