If that video really is 1-to-1 to your camera size/cropping, you might want to shift it when the player speeds up so that they can see what’s coming ahead, rather than having the player push towards the edge they’re running towards.
Done, now the camera zooms out a little and the smoothing speed is faster so the camera can keep up with the double speed. It was something I was going to do at some point, but better now than later i guess… :)
Camera movement may actually be one of the hardest parts to get right; it often requires endless tweaking here and there. Luckily there are tons of interesting articles and presentations about the subject.