I spent a whole day at the hill this year practicing riding switch, right from skating/chairlifts to bombing/carving so I spent some time recalling the thought processes when I was first learning to ride.
Not saying this will work for you, but it did for me when I was in the "get lots of mileage in now" stage. If you look at really good carving technique (lots easier in vids nowadays) or the tracks left in the snow, you will notice something instructors never cover. That is, to get on your opposite edge well in advance of your turn (ok, in reality you are carrying lots of speed and beginning your turn much earlier, but that's not the way it looks/feels when you are first getting into it).
Once you have advanced to the point you are at now, to get further, don't ride to the end of the traverse, go flat to point down the hill, and then get on the edge. Basically, halfway through your traverse, get on that opposite edge. You will continue to traverse, and then initiate your turn. People call it stuff like "being more aggressive" with your speed or approach and "commitment", but really that's all it is.
There's other subtleties like less traverse, more down, and that the edge change is really when the turn begins but I find the simpler, the better. Think about getting on that opposite edge, and then you can turn as aggressively or passively as you like.
As I say, this worked for me to get my body to do what my brain wanted. Don't know if it will work for anyone else but I figured I'd pass it along.