If you use keyhole (IMHO a good intermediary between Dan Brown and Fredrich), you can fix it between your second and third edges in 3 moves...
I first learned with Dan Brown, and the simple fact is that his method is absurdly inefficient and slow. Even as a beginner method it is TERRIBLE.
The thing he does right, however, is his explanation. It's his explanation, not his method, that makes it easy. So in that respect, its a good video. The problem is obviously that we don't want people thinking that it's a viable speedcubing method.
What actually really annoyed me was his video on getting faster. He says that there's really no faster way to do 2L other than his method (which takes 8 moves per edge insertion), and another 8 if you have the scenario OP shows us.
OP: My recommendation for you is to either learn keyhole (3 moves per edge insertion, 8 for the last one) or go straight to Fredrich. I have a video on keyhole if you want, otherwise I recommend you look for a user on YT named badmephisto, and try to learn Fredrich from him. Learning the Roux or Petrus methods may also be a good idea, or the new ZZ method. Of these I think Fredrich is the easiest to transition into and grasp for someone coming from Dan Brown's method.
Either way, now that you can solve it with Dan Brown's method, the best way to get faster is to solve it without his method.