I've tried contacting Gracy to no avail in the past. They must be too busy for commoners like me or just lazy. Used Travel With Guns and Travel Express. I recommend both.
Yes pay up front. Didn't know there was another option.
Airline depends. A good travel agent will give you multiple options. Let them do their jobs and ask lots of questions.
You didn't ask but I recommend staying at Afton House overnight in Joburg and hiring them to do your rifle permits if you are taking your own guns, which i also recommend. Mr. X or as the workers in the airport refer to him, The Famous Mr. X will get your rifles cleared and get you transported efficiently. If you feel you need help getting through the airport, Afton can also arrange VIP meet and greet at the gate for you when you get off the plane. It's not nessasary but is really nice as you go right around the lines to the front. If it is just you, probably no need. If traveling with impatient family members it is a great investment
Africa Sky will do a good job taking care of you as well although when I had rifle paperwork stolen they were not able to simply get copies sent to me via email. I'm confident today's Afton would. Back then Rifle Permits came to my rescue.
If staying at the hotel in the airport I'd hire Rifle Permits. That combo will be the lowest cost and works great also.
This all assumes your PH or Outfitter is not meeting you in Joburg as you are continuing to Port Elizabeth. Many of the good experienced PH's and Outfitters can help with your rifle permits and save you the small fee. If they are picking you up.