Lucas,
At 5'10", I'm supposedly the "average man" that the gunmakers are supposedly making their stocks for. Some time back I noticed that the length of pull of my factory shotguns was about 14 1/4", or about one inch longer than the LOP of the factory rifles that feel most "right" to me. I asked on another forum why shotgun stocks are so much longer than rifle stocks and no one could answer my question. So I whacked an inch off of one of them and found out: As the linked article notes, you want a longer LOP on a shotgun to keep your own right thumb from whacking you in the nose. So why don't rifles whack us in the nose? They will if we shoot them with the thumb over top of the stock in a "grasping" position. A rifle is properly fired with the thumb along the top of the stock, or on the right (assuming right handedness) side. Almost nobody shoots a shotgun that way because with a shotgun, the idea is to be carrying it and then whip it up to your shoulder and cut loose. Carrying a shotgun with your thumb NOT grasping around the top of the stock is unnatural at best and maybe even impossible.
The problem with a long LOP on a shotgun comes in the whipping it up, or "mounting" it, as shotgun folks like to say. With a long LOP, the butt of the shotgun wants to get caught on your shirt or coat, bringing the show to a screeching halt.
The answer to this problem is to develop the habit of, when mounting the gun, consciously flinging it forward, away from your body, and then back into your shoulder. This keeps the butt out of your clothes and off your chest. It may take you several thousand "practice swings" to build the new habit. (The "fling forward" technique won't hurt anything in mounting your rifles, either.)
If you're 6'2", I don't think you're going to like the short 13" stock, especially if it's the conventional style. (If it's the assault-pistol-grip type, though, it might work very well for you.) I'd guess that you'd be happier with the standard length stock.