I'm still not following your timeline, but I'll give it a try.

You ended up flying out to JNB a day earlier because that was all LH could book you on. The SAA service was cancelled because of industrial action. This caused extra charges to you (car, hotel)...

Your beef is with SAA (operating carrier) and with your travel insurer. EC261 won't apply in your case unfortunately since it usually does not cover industrial action. LH was, in a manner of speaking, a travel agent and cannot remedy a partner's service failure. Consequential losses (day's wages) won't be covered by anyone. You may get a letter of apology from LH, but it probably won't have the sincerity you are looking for, and SAA is in such disastrous financial shape that they will definitely not reimburse anything. I'm trying not to be too negative, but these back swan events are not well-cared for in the travel industry.

Edit: reading your post above mine, I do understand the frustration in dealing with these people over the telephone, and I don't know what advice to give you, because the agents probably weren't trying to be unhelpful, but can only do what is shown on their screen.