Why shouldn't the 7x57 be just fine for elephants? The 170 grain bullet has just about the same sectional density as a 500 grain .458 bullet or a 300 grain .375 bullet, which means that a good solid will penetrate just as far. The diameter difference probably does not mean much unless you're interested in a blood trail. While an "elephant rifle" has about twice the striking energy, this is about equivalent to 50 foot points on a white tail deer vs. 25 foot pounds. I don't think you kill elephants with energy. And anyone can shoot the 7x57 more accurately.

I've read Bell's books. I do not recall him having said it was necessary to finish elephants with a heavier rifle. And the only reason he did not like body shots--with the 7mm or anything else--was that the elephant would trumpet loudly and run, thus stampeding the herd so he couldn't shoot more than one. With a brain shot, the elephant would simply fall down, and the others would not take alarm (in those years).

Bell liked his 6.5x54 Mannlicher for elephants except that the bullets were not crimped in the cases. While unloading the rifle, he got a bullet stuck in the rifling. But he had no problem with killing power. One afternoon he shot several elephants with it, before getting the bullet stuck. After that, he only shot lesser game like buffalo and lion with it. It shot a very long 160 grain solid at about 2100 fps.

The reason he liked his .318 was that it had a 10-shot magazine. He kept hoping he'd find a situation where he could kill 10 in one place.