There’s too many moving parts here to be able to predict whether the outcome will be favourable. Going to Turkey will not help if they are added to the undesirable list by SA whilst you’re visiting Istanbul or where ever. I doubt passing through LHR without formally transmitting on the same PNR will count as a transit for these purposes anyway.
On the positive side, you can cancel a BA 241 for £35 per person, so there’s no harm in giving it a few weeks to see how the scenario plays out.
Swiss cancelled some of my itinerary (LHR to JNB) for a trip to South Africa in January - I took the chance to get a refund and stop dealing with the uncertainty. You may feel less stressed if you just cancel and take your chances with Christmas 2021 instead. I certainly feel better now I’m not worrying about whether Brits will be allowed into SA in Jan.
Edit: you will also struggle to find travel insurance that covers this particular set of circumstances. Amex Plat (AXA) won’t cover this, for sure.