I have never shot my .357" at 200m but I regularly shoot it at 100m.
I use 6.8 grains of Alliant Unique with a 158 grain round nose cast bullet. I use open sights and I do not need to give it any elevation.
I also use 7.2 grains of Alliant Unique with a 150 grain hollow point bullet without any elevation. The groups on both bullets shooting unsupported is 1-1/2" to 2".
I would expect to need approximately 6 inch elevation to hit the same point at 200m. It could be more, but without actually shooting them at that distance I can only guess.