One thing that will really help your solves to go faster is to slow down your turn speed. believe it or not, you have a very fast turn speed for a 40 second solver. you are turning so fast that you cannot look ahead to see the next pieces to solve. try turning smoothly, and consciously think about looking for the next piece to solve. One great thing about having a fast turn speed is that you can do your last layer as fast as you want. give it your all on those algs! good luck, and it's good to here that you're practicing.
I agree with this. I haven't practiced in a year or so, but I used to average around 30 seconds and my turning speed was less than half of yours. Watch the first video again, and pay attention to how much time you spend just staring at the cube. In the first ten seconds after you start the timer, you did almost nothing, and from there out there continue to be multiple long pauses. Decreasing those are where better times are going to come in.