You are better off loading reduced loads in a .357 case. Use of .38 Spl in a gun chambered for the longer .357 case gives you much more fouling and leading in the throat of the chamber.
So far as a deer load, I would run a 158 JHP as hot as you can safely get it. Cast bullets just poke a hole while the JHP will open up and impart more energy to the animal.
