That's all precicely right MidLife, (p.s., I checked out your website-- very nice!!) But I think if you tried to explain that to your average pre-solo student, you'd get the blank stare, nod with mouth agape, and they would carry on doing the exact same thing over and over again.
My personal teaching technique for power on stalls was all K.I.S.S. : set up your pitch attitute and hold it with smooth, continuous elevator travel, point the nose at a cloud, and keep it there with rudder. I don't mention aileron, because 9 out of 10 students are going to use aileron, instinctively, anyway, and the results are purt' near coordinated.
I suspect what the student in question is doing is ham-footing the rudder, causing pilot induced yaw-roll occillation after the break. This overcontrolling probably stems from stress, trying to aviod the 'dreaded spin' and can be abetted by doing a little spin recovery work. That's right-- spin the HELL out of them. Let them see what the plane does when it spins, and how easy it is to recover. Once they have a benchmark, it's much easier to judge how much rudder to use, as well a boosting confidence and having a hell of a good time!