Generally, you have the right idea of the fore-aft movement as well as your fexion-extension. This will generally serve you well until you get into much steeper terrain or hard pack that might be a little bumpy where you can loose edge hold in the bottom of the turn.
As people extend through the turn and move aft, they will naturally get a stiff back leg and this will almost always cause a skid at the tail resulting in total edge hold loss. Here is a slight modification to the above movement to help you prevent edge blowout in the bottom of the turn.
Initiate your carve with a forward shift in your flexed position just after you did your quick down unweight and gradually extend through the turn up to the apex of the turn only. Do not continue to extend past apex however. As the board passes through the apex of your turn, begin to slowly flex down lower while you are also slowly shifting your weight aft. This movement will require you to begin to flex the back leg more than the front leg. As the board crosses the fall line perpendicular to it, rapidly drop the rest of the way to down unweight and make the instant edge change onto the new edge and repeat the process. Also remember to smoothly shift forward again.
WHY THIS WORKS:
As you are hauling ass in a good carve down the mountain, you have 3 basic forces at work on your board. Gravity pulling you down the slope, Inertia from your movement pulling you down the slope and Centrifugal force pulling you to the outside of the turn.
At the bottom of the turn at about roughly the 45 degree point, all three forces combine to try to really pull your board out of the turn and send it (and you) straight down the hill at about a 45 degree angle from the fall line. This is the point where your edge hold has the most load on it and can easily break loos starting with the tail.
This is the reason for the aft shift; to add more weight to help keep that edge locked into the snow. It is also why we do not want to use inclination (leaning to the inside of the turn) when dynamic carving at high speed and or on steep terrain. We need to keep our weight stacked vertically over the edge to push it straight down into the snow.
Because edge hold is generally very precarious at this point in the turn, any bumps or harder snow can tip the balance and start a skid. By slowly flexing, we "soften" the ride and have a much better ability to absorb chatter that can cause the edge hold loss. A flexed rear leg is much much better at absorbing this chatter than a stiff extended one.
In relation to this, we want to do the fore movement early and also make sure we "complete" our turns and make sure we allow the board to completely go perpendicular to the fall line for two reasons. One, it is the only way we can regulate speed without skidding and two, it allows us to really get our new edge set solidly early in the turn. If we are late doing this, we reach apex without 100% of our possible edge hold and this sets us up for a skid through the bottom of the turn.
Happy dynamic carving....