As mentioned you don't really want to run these bullets fast, it is beyond their terminal performance limits...... keeping them to around 1800-1900 is even better. IMR 4198 is an excellent powder to do this sort of work. 300 Remingtons are in the same exact category, 405 Remingtons do not need to exceed 1500 fps.
Probably a step up with the 350 Speers, I have tested those at 2170 fps with excellent results.
For light weight more conventional bullets another step up the ladder is the 300 TSX and 350 TSX. These give excellent terminal performance between 2400-2600 fps in 458 Winchester, powders of choice change up to RL 7 and H-4198. Recently I have been testing a Win M70 20 inch 458 Winchester best results with 350 TSX and 74/RL 7 for 2496 fps at 60000 PSI, and the 300 TSX with 80/RL 7 for 2690 fps at 54000 PSI...... and mind you, this is a 20 inch gun........ And yes, the 350 TSX would be just by a small margin Buffalo Capable, with extreme care for that first shot being broadside, the next one would need to be a good solid.........
For everything less than buffalo, it is hard to beat and actually you just cannot beat it, the 250 Socom Raptor from CEB, this is a wicked wicked bullet, that would be a hammer on all thin skinned dangerous game, and everything else thin skinned, including moose and eland. This 250 performs way out of its weight class, and I have shot dozens of animals with it, including cow buffalo and hippo...... but it is at its best with thin skinned, on animals zebra, wildebeast, lesser critters, it is DRT on the spot....... Even moose have been DRT, along with bears and many others.......... There is also a 250 Socom Raptor in copper, same performance.......
I have a fellow headed to Africa in a couple of weeks with 458 Winchester, and he has his shooting 420/Raptor 450 CEB Solids at 50 yard center, with 250 Socom at 1 inch high center, he can pick and choose the bullet for the mission...........This is not common, but sometimes one gets lucky.
In my 20 inch 458 Winchester I ran these 250-260s at 2850 fps with 78/H-4198 at 53800 PSI, and they are approaching 3000 fps in 24 inch guns.....
There is no animal on the planet that you will ever need or require a 500 gr bullet for, in 458 Winchester...... the 450s will do anything you require of them........
458 is a wonderful caliber, and there are many excellent bullets to choose from depending on what you objectives are.......