We did this recently, a couple tips:
Pay for the meet & greet and gun clearance services. It's not that much money (I think ours was $200 or so for two of us) and it will save you quite a bit of time and trouble. You can DIY but after all you've spent on the safari, this is a tiny amount that was SO worth it for us.
When you go to get your customs 4457 done in the US, LEAVE THE GUNS IN THE CAR UNTIL THEY TELL YOU. Carrying rifles into a federal building can result in lots of less-than-fun scenarios. The office we went to sent officers out to our car to check the serial numbers because they didn't want us carrying them in, no matter what. They were very nice and friendly though.
Ammo limits are set by the inbound country (SA) as well as your airline, so check with everyone before deciding what to bring. In our case, SA limited us to 200 rounds, and the airline limited us to 11lbs per person - it turned out we brought WAY more ammo than we needed (like 10x as much) but we figured we didn't want to get stuck having to bash a gemsbok on the head with the butt of our rifle on account of running out of bullets
Good luck, you'll have a blast!