The one arm,standing side DB press is one of the better movements for the whole shoulder girdle. Been one of my favorites and have been suggesting it for quite a while on GetBig. After cleaning the DB from a rack/bench, hold on to a solid support with the free hand. Usually the side of a PR or post at my gym. Allows more focus on the exercise, reducing the concern for keeping balance.
Don't know what a neutral grip is, but most guys will keep the fingers facing forward (knuckles facing to the rear) throughout the press. While having the DB in line with the shoulders throughout the press (something like a PBN but with a DB) A few other guys will twist the DB as it gets closer to the top position. Take your pick, if there is any difference. Which ever way, the DB side press is a superior builder of massive delts.
ATTENTION SF: Seen a friend of mine use a 200lb DB+ for a slight jerk off the shoulders side presses ( I guess being about 5'7 and weighing 300lbs does have it advantages). Can add that to your own personal BS list, but it's true. Good Luck.