I have just checked and whilst there is limited availability on the return leg from Capetown, there are at least 2 seats available ex LHR in J and F every day in February 2011 and on some days coming back.
February is peak season on this route and also includes half term.
There are seats ebvery day in economy and so my suggestion would eb to call BA executive club and book out in Club back in a lower class. Not sure how this impacts on amex 2 4 1 voucher but the seats are there. Have you used the BA search engine for seats? this will show you where the seats are available for a whole month at a time.
There is also the option to go via JNB which has seats ex LHR every day in Club and at least 2 in club ex JNB on the 20th February.
Hope this helps