Update.
I have just pass through RSA custom with rifles less than a month ago.
We booked a night at Afton House as we arrived very late in the day, so we have selected the pre-approved importation permit service offered by Afton House for $100 US.
Long story short, we had to fill in the Saps 520 forms at home, include a scanned copy of the: passport, invitation to hunt, flight tickets, Canada (US) firearms/ammo export permit and email them to the Afton House. (Notarized copies were not required!) Their rep reviewed the paperwork and requested corrections to be made as required (apparently the Saps 520 should be already signed when submitted - page 6. I assumed that they have to be signed in front of a police officer, but that applies only if you don't chose the pre-approval importation permit).
The Afton House rep met us at the airport and took us to the Police Office to recover the rifle cases. We have been handed the Saps 520 forms, asked to open the rifle cases in order to compare the serial number off the rifle with the one recorded on the form, closed the cases and we were on our way. Technically it was quicker than it took me to type all this up. The police officers didn't even bother to stand up and look into the rifle cases. Our rep confirmed and verified everything.
$100.00 US later, it was a very pleasant experience. It might have helped the fact that we were the only group of hunters with rifle cases on that flight. Next time I might go the "solo" route since I already have a sample of Saps 520 that I know for fact it was filled in correctly. Unless we have to stay overnight at Afton House, of course.
(FYI: the pre-approved importation permit and one night at Afton House was $2,600 ZAR = $275 CAD at the time).