This is exactly what I was thinking.
You have several choices. Qatar, Emirates, and Delta.
The thing I HATE about Delta is twofold. 1.) You may not be able to get a redeye flight that morning swift enough to get you to ATL in time for the flight...so much for saving time. 2.) You have to reclaim your rifles in ATL and then re-check them in for the overseas route. Again, you're adding risks and uncertainties.
I've flown Emirates (37 hours in, about 27 hours home) many many times. Both coach and business. I consider it worth the trouble because the cattle class is just a smidge smaller than
business class British Airways USA to London. I'm a gigantic human and I'm not uncomfortable in Emirates coach.
For Qatar, the biggest fan on this forum is
@Philip Glass and he may have wisdom for you as well. I'm sure he'll say Qatar is better than the Delta approach.
Lastly, I'd like to talk about gun laws. If there is one thing a Muslim country does not tolerate, its guns circulating in their country. When you fly Emirates (I'm guessing Qatar too) they take the guns really seriously. You do your own gun permit on their website which is easy. You get a pre-approval from their Dubai security. The guns check through from USA all the way to Africa. When you get on the plane in Dubai, police and security are on their walkie talkies confirming "Mr. Smith is boarding the plane now, please put the rifles on the plane". This level of chain-of-custody is far better than any other airline I've experienced. My first hunt was half-ruined because I used a sponsor of this site to book all my airline arrangements. They assured me the guns would check through and the useless RSA flight people swore the guns were on the plane. They were not. They had to be rechecked by SAPS but nobody that knew better told me that.
Bottom line. Emirates is worth it. Qatar may be worth it too.