BA Gold here, now crediting to QF with CX with the recent changes, and have done it 15 times with another 9 more to come in the coming days.
CX is easy for doing this as you can indicate you want to credit to different FFPs for different flights in your PNR through their website and their app. This comes in handy for our cases since you can always switch the flight you're going on to each time, and won't lose your benefits.
The easiest way is to use the CX app - go into My Trips, click on Frequent Flyer Programme for the upcoming flight. Put in the new FFP number and make sure you uncheck the "I want to use the same frequent flyer programme for all flights in this booking", so it'll only stick for the upcoming flight. Rinse and repeat each time you need to do it.
As a rule of thumb you can change your FFP until boarding is complete. So, I tend to do the switcharoo when in my seat after using the lounge and using F boarding - this also mostly ensures that my BA OWE status will be reflected on the cabin crew's iPads which gets you first dibs on food choices and ostensibly better service (unless they refresh it again before departure) while I ensure that it gets correctly credited to QF.