There is a lot of great discussion and advice on this thread, helpful and educational for me and I suspect many others also. Tons of great strategies for dealing with recoil.
I have a lot of experience with a 375 H&H and some experience with a 416RM and a small amount of experience with 470NE, as well as tons of experience with shotguns including 12ga duck loads and 10ga as well.
I will simply state my personal opinion that I believe there is too much emphasis on "practicing" with a heavy rifle for Africa. I understand that guys want to be ready, prepared, etc. I don't believe big bores are designed or intended for long range sessions. They punish. On both ends. They are a very specialized tool for a very specific task. I would submit the following:
1.) Do enough shooting with your big bore to verify that it fits, that the scope mount is secure, that the action will reliably cycle and feed and eject, and that it's zeroed with your sighting system. Then put it away.
2.) Do all the dry-fire mounting, finding a target in the scope, cycling the bolt, feeling the trigger practice in the world, until your muscle memory is dialed in for that exact rifle and scope/red dot/iron sight combination. Using snap caps or dummy rounds.
3.) Get your old reliable 22 LR (suppressed is even better) and do 98% of your practice with that. Practice off sticks, off trees, free hand, kneeling, prone, off your friends shoulder, cycling the bolt, shooting slow and aimed and deliberate, and shooting fast strings. Breathing. Footwork. Sight picture. Trigger control. Reacquisition of target. Shooting within 2 seconds of your buddy saying "Get on the sticks." Shooting after walking up a hill or doing a few pushups and being a little out of breath. Shooting with the sticks at not quite the right height. Shooting at short range. Shooting at long range. Shooting at unknown or guessed range. Shooting while crouching down a bit. If you're hunting with a big bore DR, do a lot of shooting with light loads in a SxS shotgun (28 ga is wonderful) with the same trigger setup. Shoot until all the above is ho-hum.
The above is analogous to football players "thudding" in practice. This is thudding the other player without the full-on tackle that they would bring in the game. They might thud hundreds of times in practice, but they will be on ESPN if they make 15 tackles in the game.
I would argue that if you shoot 5,000 rounds a year from your 22LR and 10 or 20 rounds a year from your big bore, you will have a great experience and make your PH very happy with you.