Usually when I kill a deer with a neck shot or with a heart/lung shot, I use the first method of field dressing the animal, open throat to tail, down the belly and dumping the offal and then taking the field dressed carcass in to cool. However, when close to dark, or when dealing with one that is gutshot, like one I had this year, I never open them up and do not subject the meat to the bacteria from the gut. I just cut off the legs, split them down the back, and pull the shoulders, loins and neck meat, hams, and take the tenderloins out thru the sides, and leave the rest for the coyotes. What is left there, is the backbone, ribs, and in the case of the doe, the head and hide and guts. The inside is never opened and the meat is not subjected to contamination. You might lose 5 pounds of trim meat this way.
I guess I am never too old to learn, I took a shot that I was completly comfortable with, a running shot at 150 yards. She turned just as I shot, and I hit her with an angular shot, the bullet exploding the liver going in but angling back through the paunch on the way out. She dropped like she had been hit with a hammer, I had no problem with that, just messy to dress. Wont take an angle shot again.