Hi Phil,
I actually was thinking about this thread in my sleep last night as I recalled my horrible experience in June doing what you're attempting to do next month...connect in SA. This morning I began the process of booking my flights for this year from USA to Zim and I'm going to Harare specifically to avoid the SA overnight, connections, change of airliners, change of individual planes, etc.
I strongly recommend you take a look at what it would take to fly from USA to Harare on one carrier, then fly from Harare to your destination on a puddle jumper OR via truck. In either case you'll know if you have your guns when you land in Zim or not.
Not having my rifles cost me 10% of my hunting trip...wasted. A magnificent animal of superb quality I had to pass on. It also cost me bribes to the Zim gov't to retrieve the guns. It also cost me transport to get my guns retrieved. Losing your guns will cost you at least $1000 if it goes south in country A and you are now in country B. This after I used Steve at Travel with Guns for an additional cost of $200 as well.
Bottom line, minimize connections, minimize air line companies, minimize layovers. Get your guns back in your possession as fast as humanly possible.
-Rookhawk