ok. No 2f1 involved and a solo traveller.
Realistically this isn't going to be bookable (all 4 sectors) in F, in one go. You may end up with 4 sectors in F, but it'll take perseverance and a lot of luck. To be honest, the word compromise will be needed.

Try booking 1 sector at a time, if and when availability opens up (I would book WT+ or CW if they pop up on the days you prefer - just to lock something in).
If you are very lucky F (or CW) might open up about 2 weeks before travel. In your situation I'd keep an eye on San Diego (SAN) and Johannesburg (JNB) as alternative routings to settle for.
CPT-LHR drops to a single flight from 31st March. You will not get CW or F on the next few flights from then.

Oh, and be prepared for the phone and cancellation fees. If you are calling to change a WT+ to F I'm sure you'll feel it worthwhile.
Me? I'd feel lucky if I got CW, F, WT+, F on the 4 sectors with one leg being JNB.