All your cartridges mentioned shoot their bullets quite fast, they are all calibers I would see on the more open plains in the Kalahari, Karoo or in the mountains of the E-Cape.
Think of placing your quarry in one of the 4 classes and then choose accordingly.
1. Small to medium game at around 100m - Impala, even Kudu.
2. Small to medium game at around 250m - Springbok, Black Wildebeest, Red Hartebeest
3. Large game at 100m - Eland, Blue Wildebeest
4. Large game at 250m - Eland, Gemsbok, Zebra
Take any caliber and think about it..
257 Roberts , ideal for 2, great for 1 and maybe at a pinch it can do 3 with perfect placement and bullet contruction.
4 becomes a problem with having to do that perfect placement with the added loss of energy.
The fast 7mm's dont really offer much less recoil than a good .30 cal like a .30-06.
A slower 7mm like the 7x57 is great but again its a stretch for class 4.
The common 300 magnum recomendation is based on covering all 4 with one rifle.
I use a 6.5x55 for the majority of my hunting these days, but have got a 9.3x62 for Eland in the Bushveld but am happy to use that for everthing under 150m. I still need a 7mm or 300 Mag to do class 4.