I took an SKB gun case and packed a lot in it. Bow, doz arrows, broadheads, everything I could get in it. However, one thing you need to do ! Tape a sign on the outside "ARCHERY EQUIPMENT - NO FIREARMS" This was suggested to me and it worked like a charm. I had no problems. I also put the TSA locks on it. That was if needed they can check, but you shouldn't have any problems. Book all your luggage all the way to your final destination.
If you haven't book your flights, I highly recommend Lori Ginn with Travel Express. check it out at travelexpressagency.com. She does a great job of getting you there and back. She can also book your motel stay over there as well. She will take a lot of stress out of trying to make connections. She also shops for the best buy on airlines. Just a note - for the long flight over to Africa, I paid a little more for an exit seat. There will be no seat right in front of you and gives a lot of leg room. If you don't do this, you will be sorry on a 16 hr flight. Give Lori a call, you will be glad you did. One of our flights had been cancelled and we didn't know about it, but she was watching and got us rescheduled right away.