I took CX instead of QF on my SYD-HKG leg without any problem...the CX check-in agents gladly took my ticket and issued me a boarding pass.
However, on my HKG-LHR leg, it's a bit more complicated. My original ticket was for CX 255, departing around 00:45 (after midnight)...however, I tried to take BA 26 instead, departing 23:25 (thus considered the previous day).
I went to the BA check-in desks at HKIA and used a Club World check-in desk (for some reasons they have quite some passengers waiting at the 2 First counters...do they really have that many First and/or Emerald passengers? It seems to me they are just using the F desks for some special cases, and real F/Emerald passengers need to queue somewhere).
Anyway, the agent took my ticket, was a bit not sure what to do, and so went to talk to their ticketing desk (a few counters away). When she was back, she told me that since my ticket was for the "next day", I do need an endorsement from CX. I then said, as far as I know with this OWE ticket I don't need any endorsement, and asked whom she asked to get this answer earlier. She then said she got the confirmation from the ticketing people and they said I do need an endorsement.
I then said, ok, if you really think I need an endorsement, I don't mind going over to the CX desk (FYI - CX and BA are at exactly 2 different ends of the HKIA - maybe a 10-15-min walk)...but then I will not come back to your BA desk, I will just take CX HKG-LHR instead (knowing that CX is wide-open that night). Then she went to talk to the ticketing people again, and came back and said sorry, we made a mistake, you indeed do not need an endorsement. She said sorry in the end again on this.
And, I also did call CX and cancel my HKG-LHR reservation, just to make sure that they won't consider this as a no-show and cancel my SFO-HKG a few days later on the same booking.