When I posed this question to Adrian Underhill he was kind enough to send me the following response which I think is worth sharing:
No need to ask sts if they know the chart, because they don’t. Same with teachers, they don’t either. It’s like asking “Do you know English Grammar?” It is not something you know. You have met it, you know some things quite well and other things imperfectly and loads of stuff not at all…and you are ready to learn more….If the teacher is willing and able. The chart is not something to know. It is a whiteboard on which one brings to bear the third language system,(Grammar, Vocab, Pron) in order to integrate it into all the other language work going on. My advice is in the first lesson take them for a flight over all the sounds, so they can see for themselves what is there, and what they already know and where the issues are to be worked with, Then you get them on your side, and they can start feeding pron to themselves, rather then rely on occasional pron crumbs from the teacher’s table. So I suggest you let go of imagined limitations, and instead of maybe managing to teach schwa during the course, expose (not teach) all the sounds in the first day, then they are all in circulation, and that alone will change everything in the following days. Multilingual class is ideal. They all have something to work on. To student 1 you say, faster, to 2 you say clearer, to 3 you say join the words to 4 you say where is the stress, to 5 you say less energy please, to 6 you say what’s the first sound, to 7 you say what is the second word, could you say it slower, ok where is the stress, to 8 you say say it as if you mean it….and so on….. All can be challenged to do one bit more than they are doing. They don’t need you to teach each of those things, they just need the instruction and maybe a little assistance, and the others learn from hearing all this going on. A very rich environment.
Here is what I find works:
Be sparing with explanation
With small bits of connected speech get students to identify just the tonic syllable, ie the syllable on which the main meaning rests and on which the main intonation movement seems to take place (even if the movement is spread across others as well). Never mind which way the movement is going.
Get them to identify other stresses and unstresses.
Get them to join the words smoothly.
Get them to imagine and visualise the feeling they want to express
And rehearse it in their mind’s inner voice
Then say it aloud. And be struck by any difference between what they rehearsed in the inner voice and what they said aloud.
Try it again
In summary, my cardinal rule: spot the tonic and play with it. The rest follows.