I'd use the 7mm on Nyala. If the bullet is suitable for the velocity and game animal.

No need for the .375 unless you're hunting something much bigger as well.

If I was hunting Nyala plus assorted plains game in Natal and hopefully will one day, I would take either a .30-06 again or the 8x68S. The 8mm merely because it is supposed to be my "world" hunting rifle and is more than capable on various plains game and flat shooting.