I've carried a Rem Model 700 Classic in 375 H&H Mag to Africa 5 times. I've also shot a 458 Lott built on a Rem Action. These are push feeds. I have never felt they were an issue when after heavy game in Africa. It has to be pointed out that if the first round is on target, then the ability to cycle the action isn't too vital. Only on a bungled shot or an encounter with a herd would lead to potential problems. The first is the fault of the shooter and the second is a very rare thing.

I've tried to make my 375 fail when cycling the bolt. I've even held it upside down and have never seen it fail. My Rems are very accurate and I know I can put the round where I need to put it. I personally wouldn't hesitate to hunt with a single shot as long as it is accurate. The CF vs. PF is an argument designed to sell rifles and it has very little to do with taking game in a hunting situation in today's world.

Both work. Both are dependable. Use whichever one is best for you.