Send that last round aiming at the middle of the front end. At this point with an already wounded deer you are just trying to kill it in a shorter time than starving/dehydrating to death.
The good '3 shot group' rifle isn't going to miss a full deer at 350m even on the 10th shot if you know basic shooting fundamentals and can apply them at the time of the shot.
This senario may happen to you one day even with your good 10shot group rifle and it still might get away... Welcome to real life hunting and old 'Murphy's law'.
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