I am a big fan of the 8x57 in both its rimmed and rimmless forms. I assume you have verified whether you have a .318 or .323? Both the S and J are found in rimmed form. I have used a rimmed .318 in a drilling regularly for three decades and have taken everything from red deer on down with it. I tend to shoot heavy for cal bullets (196 gr), for which many of the .318s were intended, and I get MOA groups with the scope in place. In such configuration, it is a 200 meter weapon and would be a fine plains game cal. In fact, I shared seating out of Frankfurt with a German hunter in route to Windhoek two years ago who was bringing his trusty drilling in 8mm.
The double rifle angle is a bit more complicated because you will have to find a load which regulates well. Sight and proof marks unseen, I would bet it is a .318. Regardless, I would start with the heavier S or J bullets. Open sights are a function of the rifleman and the terrain. I would hesitate to bet a whole safari on such a rifle - from a guy who is bringing a paradox sxs as his second gun this summer. No matter how many leaves you have, anything becomes a bit risky much beyond a hundred meters. You will pass up some good trophies by so limiting yourself; or greatly increase the risk of wounding game - and remember, in Africa, with a drop of blood you have bought it. On the other hand, as a second rifle once your main quarry are in the salt, it could be a lot of fun. As I say, finding the right load will be the real challenge.