Why the Angels are not moving once no more characters are looking at them sometimes just shows that they are innately sort of meta characters themselves. The audience in front of the TV counts as an observer. YOU are still watching them until the camera cuts away of course.
If not for that mean an-image-of-an-angel-becomes-an-angel-trick this would be a way to imprison them effectively.
Point a videocamera at them and leave it running. At the end of the day watch the whole day in fast forward. Even though no real person was watching it at the time, you are now and the Angel shouldn't be able to move because of that.