Just did up some calcuations to work out the ease/difficulty to get OWE status using non-QF OW flights. Using SYD as the base, I've put in CX MPC, BAEC, and AAdvantage as comparisons to HKG, SIN, and LHR.
For HKG on CX flights, QF requires 24 one-way J trips. CX = 21, BA = 11, AA = 15
SIN on BA, QF = 24, CX = 25, BA = 11, AA = 18
LHR (1 flight number) on BA via SIN, QF = 10, CX = 10, BA = 7, AA = 7
FRA (2 flight numbers) on CX via HKG, QF = 10, CX = 10, BA = 6, AA = 7
Note 1: decimals are rounded up to the nearest full number (you can't really take 0.3 of a trip)
Note 2: If QF coded flights are used, the numbers for QF would become HKG & SIN = 12, LHR & FRA = 5 on business. Flexible business require one less one-way trip for the 2 Asian cities, and remain the same for the 2 European cities.
Note 3: If I made a mistake, let me know and I'll update.
EDIT 1: LHR on AA corrected to 7.