My total trip was 13 days. The trip started from Austin to Atlanta direct to Johannesburg. If you are flying this is the best / shortest way. 13 hours going and 16 hours return flight to Atlanta. I learned this the hard way.
I spent 3 days in the bush at africantrophypursuit.com and then traveled to Sodwana bay for some fishing 3 more days in semi Bush, and another amazing experience on the Indian ocean. I would also highly recommend my friend Johan and his wife at
http://seevarkie.co.za/ for an experience of a lifetime. On pricing on the fishing, note our dollars will buy a lot of fun right now, with the dollar very strong to the Rand ie: 1$ to 15Rand or higher.
http://seevarkie.co.za/rates.html Rooms and fishing rates are very reasonable. The main reason for a short visit was to sample other areas of the country.
Meals there are very reasonable, and good compared to here. A loaded breakfast cost 65 rand for example, roughly $5.00 US in a nice place in Pretoria.
Sodwana is a 9 hour drive from there, but was worth the trip. It sits in Sodwana Bay is part of the iSimangaliso Wetlands Park which was proclaimed a World Heritage Site due to it's uniqueness with no commercial fishing, undeveloped beaches (highest dunes in the world) as well.
The drive to the Ranch from Johannesburg was about 3-4 hours, on good safe roads. Bear in mind, they drive like the Australians there, on the left. Speed limits ranged 50mph to 75 (80 to 120km/h)
Depending on the game you are after, it is priced accordingly; as listed here;
http://africantrophypursuit.com/prices
AndyC would probably have a lot of advice, being from the area as well.
With respect to getting a single trophy done, they can combine a shipment to the US with other shipments to reduce costs.
I will work up a breakdown on my total costs, and taxidermy. The rates were really quite reasonable, and service top notch. To answer your question more directly here is a scenario from another client;
Marquetta had a 7 day safari and shot 9 big trophies, (including the African Super slam in one trip). The ASS is the Kudu, Nyala, Bushbuck and Eland(the 4 spiral horns they have in Africa). They are also very pricey animals. She spent $2500 on airline tickets, $13000 on total safari bill. $2000 on dip, pack and shipping of the 9 trophies, and expect to pay no more than $600 a piece to get mounted in the US The guys at Africa Trophy Pursuit are a great place to finish your African super slam! As they have the spirals you seek.
My guide, Freddie, who was totally amazing has successfully hunted the ASS 8 times with clients in one trip that wanted it.