How mild of a load in a 44 do you want to go? I have a what I call my rabbit load. It is a 215 grain swc cast of ww. Over 6 grains of Red Dot. My guess is around 650 to700 for velocity. Shot many rabbits with it. Then one day I had a big meat dose stop about 100 yards from me when I was out of my truck. I had the window down so I reached in and grabbed my 44. As I was aiming I remembered it was loaded with my rabbit loads. I aimed a little higher and hart shot her. One leap and it was over. Would I have tried a shot with a hot 357? No.
Steve