Try searching for flights to Johannesburg, and then buy separate flights from Johannesburg to Cape Town.
Johannesburg is generally much cheaper on paid tickets and yes there seems to be some award availability.
I am not able to afford J or F class, and I go to SA frequently as I am South African.
In November this year I am planning 2 weeks in SA mostly in Cape Town and so I have purchased an ex-EU from Amsterdam to Johannesburg in Y, about €390 return. Added on some cars and hotels to make it a BA holiday booking. I then booked my internal flights separately. Johannesburg to Durban to Cape Town to Johannesburg was approximately £125. again in Y. As silver, it’s unlikely that I will get any upgrades but you never know.
Special Services have previously been extremely helpful to me, and I expect if I have any problems they will assist again.
Whilst I am travelling Y, and you are looking at C, I hope I have given you some help.