I think the answer lies within your definition of "ultimate stopping". To me, that implies a charge; and you listed elephant, cape buffalo, rhino, and hippo.
If your scenario imagines a caliber which would stop any or all of those regardless of shot placement - it doesn't exist in anything you could take with you into to field. The same applies for a harvest shot.
"Ultimately" - it's a combination of placement and caliber. You need a rifle which not only shoots accurately, you have to shoot it well - meaning both accurately and possibly quickly. Secondly, your bullet has to have the energy to penetrate bone and do damage once it gets there.
There are plenty of discussions on this forum covering the attributes of the multitude of calibers and bullets.
If you are picturing yourself in a situation where one of those big boys is coming straight at you, wounded or otherwise, you are engaging a moving target and off sticks.
Others may disagree, but for me, you need a rifle which you can shoulder quickly while acquiring and maintaining your target, and shoot confidently.
My choice is a double with iron sights; you can acquire your target and maintain situational awareness, and you have the option for a rapid second shot while holding on target.
If the animal is close, there might not be time for a second shot.
"Ultimately" - it's the Indian not the arrow.