I don't agree with advice you were given above. Your contract was with CX, with BA only being your agent in the process. CX have changed the schedule, it is up to them to re-accommodate you. BA will not take the financial hit of rebooking you in UL J if there is no award space, just like a travel agent wouldn't.

Where you are justifiably frustrated is that as your agent BA need to change your ticket so they need to liaise with CX to have you re-accommodated. I have had no trouble with a similar situation booked through AA who put your request though "industry liaison" but BA don't seem to care or know the process. It might be worth calling CX: if they acknowledge they will re-accommodate you via HKG but BA need to liaise, that may help your discussion with BA.