...can you bring them into Zimbabwe?
From what I'm reading, you can, you just need proper SAPS paperwork. Again, I'm a bit short on details, since it doesn't much apply to me, but I'm working this stuff real-time, so I'd be happy to ask.
Also, on South Africa, it seems there is some misinformation. That country documents their strict policy of 4 guns, no semi-automatics, and no duplication of caliber. But, it seems to apply much more to rifles than shotty guns, as the outfitter's documentation goes on to say,
"For Semi-Automatic shotgunsor handguns, you must supply a letter of motivation stating the reason for wanting to bring a semi-automatic/handgun to hunt in South Africa. It must be an original request; with an acceptably good reason otherwise consideration will not be granted. If you wish to bring a Semi-Automatic shotgun for bird shooting, or a custom made handgun the application should arrive 35 days prior to arrival at the Agents office."
"You are allowed a maximum of four firearms, not more than one of the same caliber. (An exception to this may apply in the case of shotguns where more than one of the same caliber may be allowed for bird hunting if an acceptable letter of motivation accompanies it)."
All this "may/acceptable" talk leads me to believe that hiring a firm that specifically deals with gun import is the way to go. My situation is going to be a bit unique for a number of reasons - so I've just decided to head that route.