I don't want to take us off topic . . .the OP was about both the rifle and hunting elephant. Many have chimed on on the rifle - one I am most happy to watch others shoot. I have used .375 on elephant and felt a bit undergunned. .404 or .416 would be just about right.
As for the elephant part of the story . . . I have often thought of hunting tuskless because the cost is much lower than a trophy elephant and the experience is much the same (if not more thrilling because of the nature of these females). Having said that, I have over the years developed doubts about such hunts (I was going to say the ethics of such hunts but I will keep that loaded word out of the discussion). Killing females from a "family" group - which is where they will be found barring some unusual circumstance such as the dying cow in the story) undoubtedly has an impact on the remaining elephant, both females and their young. And I have little doubt that the impact is wholly negative, and will show up in future interactions between members of the herd or the offspring, if and when they go off on their own.
Given the social structure of elephant, I wonder if hunters are best to limit their hunting to bachelor groups (which tend to be small) where no young are present. Shouldn't we try to limit the impact of our hunting on those animals which are not hunted? I realize taken to an extreme this could mean not shooting a big impala ram from a herd which included females and young, which would be impossible. But in these other cases, at least in my experience, the herd eventually calms down and no long term harm seems to be done. Perhaps this is a result of these animals being used to other animals in the herd being eaten . . . an experience elephants rarely have?
So as thrilling as this hunt was, I do wonder about the long term impacts of taking the matriarch and two other females out of a herd? Aren't dangerous and ill-behaved elephants are usually the result of interactions such as these, rather than of nature on its own?
I'd be curious to hear from some of the PH's who regularly hunt elephant and tuskless in particular - am I right or wrong?