Well both the 357 and 44 are quite capable of 200 yard shooting. The 460 will add blast and recoil and accomplish little more.
Spend the money on an FA in 44 magnum and don't look back. The old adage of cry once. I shoot my FA in production class for IHMSA on occasion. 357 magnum, case full of H110/296 and custom 220 grain LBT. It stays supersonic all the way to 200 meters. Average group iron sighted is about 3MOA IF I am on my game.
Buddy has the same in 44 magnum, same result with more recoil.
If you go with one of the single shot platforms, that is a whole new ball game. Quick and easy, get an encore and a 308 barrel. Recoil is very manageable.
i run the same load in my 308 pistol as I do my rifle, Varget and a 150-165.