I did this in March: Qantas operated flight to JNB and BA on to LHR.

Just my thoughts on your plans:
I was at SYD early and had a delightful breakfast in the F lounge. Great service

I'd never go on a SA operated flight (have done it once)

BA lounge in JNB was nice and not crowded. Not in same league as Qantas F lounges in SYD and MEL, but then it is an out-station. The BA business lounge was open much earlier than the F lounge, and that day the food & drink offerings were identical

Don't bother going landside at JNB. Huge terminal but little to see.

BA F is inferior to QF F . The flight to LHR was full and service was not great. There was certainly none of the "dine when you like" promised and the meal service took ages