I've been to africa 5 times and have killed at least 5 animals each trip so I have some experience there. Some great advice above on vitals on animals. The first question is WHERE will you be hunting? North cape or East Cape vs the Limpopo in RSA would affect my decision. Much of the North Cape is open and longer shots are likely going to present themselves. That being the case I'd use the 156 Berger. In the Limpopo you are probably going to be in the bushveld. A long shot might be 150 yds and the Norma might be the bullet to use. Even if your getting 2 inch groups at 100 yds... Or an AB or perhaps a a Barnes.
Then you need to consider your species. What animals do you intend on hunting with the 6.5? A Kudu is as big as or can be bigger than a bull elk. How about an Roan? 2nd biggest antelope in the world. Wound one and you pay a trophy fee of $4-$6K. So I'd use the .375 there...... What I'm saying is use enough gun. Will a 6.5 whatever kill a roan? Yes it will. Is it ideal. No its not. So look at your animals as well as your bullet.
In the past I've used TTSX's and AB's. My last trip I expected some longer range shooting. I took my 7 SAUM with 180 gr Bergers. 15 one shot kills including 2 cape eland (487 and 513 yds). I used 2 on a Pattersons eland that appeared to weigh around 2000 lbs. He was getting ready to go down when I hit him the 2nd time. I was going to use my .375 on him, but circumstances changed how that went down. I hunted both RSA and Zambia that last hunt and a buddy used my rifle in Zambia also to bring up the animal total.
The Berger 156 is a new bullet, but likely the one I would take where any longer shot might be offered. I have had good results with them and have read on here of others doing well with them. Then perhaps the AB as my second choice. I have never used a Hammer bullet. I have been tempted to. They likely would do well for you also.
If you have not joined over to africahunting.com then you should do so. Lots of experience over there on permits, rifle transport, travel in africa, trip prep and getting trophies home. Good luck on your upcoming hunt. I hope its for 2021. 2020 sooner than Sept may not happen.....
Bruce