For the uses contemplated, I would also recommend the 375 H&H Magnum since it's a bit more flexible than the 458 Lott and the 416 Rigby.
The "extra step" in loading the 458 Lott is the belling of the case mouth which takes very little time. Since you will never need to trim 458 Lott cases, the extra step is much more than made up for with the time you save by not trimming cases. If you use carbide dies, the 458 Lott cases also require very little case lubricant so it's less messy. Also, with the Lott, case life will only be limited by when the mouths start to split; in other words, case life with the Lott will be better, probably a lot better, than the other two.
I don't have any experience with the 416 Rigby so I can't speak to that cartridge. What I can say is that the 375 H&H Magnum, in my experience, at 100 yards will shoot 270 and 300 grain bullets and bullets of different design to about the same place. The 458 Lott will have different impact points with different weight bullets. Of course, the range of weights of bullets in the Lott is quite a bit broader than what you get with the 375 H&H Magnum which probably has something to do with it. The 375 H&H Magnum is also not abusive to shoot; many would consider the 458 Lott abusive.
You will also probably get better accuracy with the 375 H&H Magnum than with the 458 Lott and the 375 H&H Magnum because of the bullets available for it and the ballistics is a more long range weapon. I would consider the ideal maximum range for the 458 Lott to be about 150 yards and that of the 375 H&H Magnum to be about 250 yards. With practice and knowing where your gun shoots you can, of course, push these ranges a bit.
