I'm far from being an expert, but in my experience I find alot of newer riders tend to move around too much on the street, before really becoming comfortable with leaning the bike.
The purpose of hanging off the bike is to re-position the center of mass lower and to the inside of the bike, this will allow for greater speeds compared to the same lean angle with an upright riding position. When getting on the gas hard out of corners, hanging off also allows you to get the bike more upright, providing better traction than would be available on the side of the tire. There is a finite amount of traction available at the limit, and you have to balance that between braking, turning and accelerating. Hanging off might become necessary on bikes with ground clearance issues when lean angles increase, to prevent from dragging hard parts.
My triumph probably has similar ergos to your 599, albeit a little more stretched out. I ride with the balls of my feet on the pegs at all times pretty much. At first it was to keep my toes from dragging the ground, but then as my riding progressed, it allowed me to firmly plant my wieght on the pegs, instead of "sitting" on the bike. I support most of my weight with my feet, my knees on the tank, and my core, keeping my hands very light on the controls. With your feet and body in a different position, you may have to adjust the shifter/brake levers to accomodate this new riding style.
The most important things I can stress are to practice good visual techniques, i.e. reference points, and stay loose on the bike. Look up Keith Code's "Twist of the Wrist" and
The Pace for some good reading.
and if you ever want to ride, hit me up