Let's start with literal casting. Imagine that you are standing at six o'clock on a watch. Your dog is in the center of the watch where the hour and minute hands meet. Imagine further that the bird is at 10 o'clock on the watch. The literal cast would be where your arm is at 10 o'clock - or a slight angle back cast. That is, if the dog responds perfectly to the literal cast and carries that cast without deviation, the dog would line directly to the bird upon taking the cast.
I disagree with the description that you - and others - have given for a momentum. I don't think anyone is right or wrong. It is just what the term means to each of us.
To me, a momentum cast is simply any cast that is intended to change a dog's momentum. It could be a cast to drive a dog out of a spot. It could be a cast to break a dog out of yo-yo. I guess you could say that the cast is intended to obtain progress to the blind - but that seems a bit narrow to me. Again, to me, a momentum cast is a cast that is intended to change a dog's momentum. To me, the term does not imply precision.