Mouth grunting at a deer puts them on high alert IMO. Now he's trying to pinpoint where the noise came from. There's a difference between a deer looking over the area and a deer trying to find you. That's why I NEVER grunt to stop a deer running or walking at a fast pace. If the deer doesnt' present me a shot naturally I'd rathe let him pass then to intentionally stop him putting him on high alert. Like you said they can jump the string or bolt at any second no matter how fast your bow is. The picture in this scenario to me looks like he is just glassing the area checking it out, but not on total high alert trying to find you.

This is a tough one kinda, but If the limbs aren't a problem I would probably aim for the lower 3rd of the kill zone and he should drop right into the arrow.

that deer would be down in my book