It's worth noting that the CAA is in Pretoria, so if you want to submit paperwork in person, you need be in Pretoria too. It's perfectly possible to hop on a budget airline in the morning (from, say Cape Town), hire a car for a day, do the CAA thing, then fly back in the afternoon, although that does add more cost.
I believe there are expediting services in Pretoria you can courier your paperwork to, who then go and submit everything in person for you, but I have no idea what this costs.
My experience of the SA CAA is that they're fantastically helpful, if you tell them exactly what you need and give them some notice. I ended up organising a courier to pick up the validation documents from them (having done all the applications from the UK in advance), resulting in me having my paperwork in my hand on day 2 of the holiday. I strongly recommend getting a phone number for whoever is dealing with your application and checking in with them periodically.