The .375 will work reasonably most of the time, and it is preferrable over the .458 winnie.
If you must own a .458, you may wish to ream it to the .458 LOTT, depending on the rifle and or action.
The two .458 winnies, I have worked with were OK, but one of them was not worth the trouble.
Sometimes they are good, sometimes not.
That is the .458.
I imagine the .375 will not be a problem at all.
I have heard of splitting stocks, but I think they have dealt with this issue a good time back, as they were doing this repeatedly in the 60's.
They should be better now from the factory.
The same time, during the 60's, is when the damn winchester .458 ammo was horribly bad off.
They, I am sure have upgraded the quality control.
Both on the rifles and ammo.
Especially Hornady ammo, which is wonderful now.
As for the rifle, the most you should have to deal with is the feed ramp, loading, ejection, etc., as to make it smoother, but this is with all of them.
Recoil will not be bad with the .375 at all.
The .458 is a bit more, but tolerable, if you don't have to repeatedly shoot. Which you won't anyway.
They are both small cartridges, compared to what CAN be had.
There is no harm in either, although, I would opt for the .375 first and foremost, due to versatility, and the 300 grn. solid being able to drive deep enough in most cases that you might encounter if the shot is placed correctly.
---coltnavy36---