I think the pronunciation of individual phonemes is the most important part, rather than simply intonation alone. Both are necessary.
The descending staircase of intonation is not something I see as accurate, except that is how we do lists, for example, while ordering a pizza. Sentences, however, follow an olympic podium type order, 2 1 3, if you follow, but our intonation overall is very very flat.
I think a course in American phonetics, including the actual phonemes we use, will make your students cognisant of what to listen for, and will help them improve their own accent. If you start with intonation, which is starting with the "fine tuning," then what will they think of the "coarse tuning?" They might not become aware of it.
Hope this helps a bit.
Student or Learner