Well, that was relatively painless in the end.

A 50-minute Skype call to AF's UK number (during which I only had to mention the words "Article 8" once) and the refund was processed, including my seat reservation fees.

I am now rebooked with a multi-city BHX-JNB//PLZ-ZRH on a combination of LH, SA & LX, with ZRH-BHX filled in later. This was an extra 120GBP or so, but saves me two days of driving.

Thanks to everyone for their input.