Charlie congratulations on making this happen!
Talk to your outfitter and PH about how the hunt will go... Walking up to wild elephants is an experience to not be missed! Get in close, at least within reason... That 416 of yours is plenty of gun, shot placement is vital but the 416 offers a tad more leeway over a 375 as it has enough extra shock to knock the beast down if you are off just a bit.
If at all possible, get your PH to let you set up and practice aiming on an elephant before the time comes for the actual shot. This is a time when you don't want to be shy about another guy whispering in your ear! Have him talk you through it and onto the point of aim. Watch some of
@Ivan Carter videos and how he does this... This is something I did not get on my hunt, even though there was opportunity, from my perspective at least. When it came time for the shot, that was the first real aiming at an elephant I did and the PH had to be watching another ele off to our side.
As you mentioned this will be a once in a lifetime for you... That means that first shot is likely the most important (and expensive!) shot you will ever take in your life!!! Get the most out of it.... A guy like Ivan seems to really "get it". There was one episode where he has the guy practicing on the first elephant they walked up on and he has him going through all the motions, explaining exactly where to aim, then whispers to chamber a round, take off the safely and squeeze the trigger... But the guy was calm and made a great shot because he was taken though it calmly and orderly.... The opposite is a PH who tells you to shoot quickly at an animal you never aimed at before and then criticizes you for a bad shot..... I did not have either one of these experiences but some practice aiming would have been nice when we had the chance days before.
I was superbly impressed by the performance of the Federal Premium Hydro Solids I used.... I'm sure your Hornady solids will be fine but if you want that bit extra, get one of the guys on here to load some up for you.
I suspect you are completely comfortable with that rifle and scope combo you have.... But practice as best you can. I could not safely practice the upward angle and would have liked to take a course down in Texas or the like.. But I was out of time. so I set up targets at my range at 25, 50 and 100 yards (my only options) and I would practice shooting at all ranges off sticks and off hand and to shoot as fast as I could while maintaining accuracy. Especially as I was also training for a buffalo. You are doing this right having done both lioness and buffalo first! You should be well prepared but practice those off hand 25 and 50 yard shots. Especially good accuracy offhand at 25 yards!
Then be as prepared as you can be for the most incredible mixture of emotions as you bring that huge and majestic animal down in one shot at close range! Quickly reload and be ready for follow ups "just in case", your PH will be there to let you know if he wants another shot in but it goes down back legs first, your likely done. Anything else, get another couple shots in and do it quickly. You owe it to this animal more than any others to get it done correctly and quickly!
And start working out as best you can, this should be the most physical hunt you have ever done other than maybe a mountain hunt. But don't think an elephant won't go up a mountain! We tracked then right up the biggest steepest hills around, I was on all fours with my rifle slung over my back climbing rocks up a hill right on their trail of destruction. They are incredible animals! Hunting is the only time you can really experience the full thrill of getting in next to these beasts! But it can be very physically demanding. You can do an elephant hunt out of condition, but the more you can do, the better the experience will be and the more likely you are to get the best animal.