Getting from classroom to conversation with "corrected" pronunciation of a word or process is the focus of HICP. Should you need a mathematical model of the main variables involved, the "Theory of planned behavior," first articulated by Ajzen, puts it this way:
Now I'm not entirely clear on all the variables there ('BI' = behavioral intention, what the desired performance should be)--you can go to Wikipedia and unpack the entire formula, yourself--but, were we to apply it to pronunciation change, one of the more important variables would certainly be 'p' (perceived power of control). And by that I don't mean that we simply provide students with a list of suggestions for as many possible integration strategies as possible and then send them home to figure out a plan as optional homework--and then find some native speaker to practice them on. Granted, you can rather easily create a temporary "perceived power of control" in learners with attractive exhortations and visual/cognitive schemas, but the sense of control ultimately must come from the "felt sense" of successful integration. One of the great discoveries of Alexander before the turn of the 20th century was that change in speech behavior can often be best accomplished by body-based interventions outside of social engagement. In our terms, homework done in relative isolation becomes the bridge to enhanced social functioning. Before I post my new one, how would you characterize the (implicit or explicit) steps, phases or benchmarks in your BITI (behavioral intention to target-level intelligibility) model? Even a little BITI is better than none . . .