You can load them all down pretty easily, the only question I have is which .416. I have been working on loading the 416 Rigby down with cast bullets and been having an interesting time of it. Not much out there and what I do find really doesnt happen in my rifle, the same as what happened in theirs. Anyway, if it is a Rigby I've had good luck with AA 5744 and a RCBS 350gr FN gc. Take a look at their manual for loads. I,ve also been loading an LBT 360gr LCFN gc using Hodgdon 50BMG powder. While I haven't got "THE" load for it as yet it has a promising outlook. This though, is not the all purpose rifle your looking for.
As far as the rest, these are taken from Handloader #177 FEB/MAR 2000, a Ken Waters article.
.375 H&H, 235gr Speer IMR 4895 65gr for 2463fps & 3165 ft/lbs
250gr Sierra IMR 4064 62gr for 2454fps & 3342ft/lbs
.458 WIN MAG 300 Hornady H.P. IMR 3031 55gr for 1869fps for 2325ft/lbs (I'd personally use a cast bullet)
There is, of course more, I would just get the back issue and check it out. I've personally have used his Deer loads in my 300 WIN MAG & .338 WIN MAG. They really are tame compared to what they can be.
At one time I would have said to go with the 375H&H, but after a trip to Alaska a few years ago myself, and able to pick any rifle to go with, I settled on the .338WIN MAG, to me at least, it has everything you need for success on anything your looking for. My opinion and mine alone. Good luck and may GOD bless you on a full recovery. CRASH87