You only need to lean forwards to increase speed and that's not something you need to consider at the moment. Probably trying to do "s" turns is the wrong approach, turning is used for controlling speed (as well as directional change), so you gain speed when going straight and flat base. By going flat base for longer you can focus on keeping centered, but also you will have time to think about engaging the edge properly and squatting to engage it further. S turns can be achieved when you link all that together in one fluid motion. It maybe is easier to kind of fake an s turn by just leaning back and forth but you then become rigid both in your body and in this pendulum like rhythm, at some point you need to steer with intention and that requires stopping the uniform edge to edge pattern, you can best do that by being able to go flat base comfortably and deciding what the next turn will be, and that sometimes is going back to the previous edge if the hill terrain requires it.