RE: Stop him first or not?
I prefer not to shoot moving deer and have stopped many deer without issue. I did spine shoot a doe that I had stopped at 12 yards when she tried to jump the string. I guess if a deer is close and moving very slowly with its head down browsing it would be better to not put it on alert. A deer browsing stops and pauses as it walks anyway, so it should be just like shooting a stopped deer.