The PronSci approach and materials reflect other insights that Phonetics can offer teachers of English.
Catford is a primary source for two of them. His analysis (e.g. 1977:220) of reduced vowels (like schwa) when they lie between two consonants has them as 'open transitions' rather than true vowels. They therefore contrast with 'closed transitions', where the articulations of the consonants overlap. Contrast police and please, terrain and train, as examples.
Catford also insisted that sentence stress in English was due to greater effort being made by the speach breathing apparatus (which he labelled the 'initiator'). This traditional analysis of stress has tended to be lost since the advent of easy recording and speech analysis technology which has led to analyses of stress that emphasise its acoustic characteristics. (Very recently, though, there has been a resurgence in Phonetics in the understanding that in English, stress=loudness, with greater loudness being the result of greater effort being made by the speaker.)
Honikman (1963) brought back into the English language literature the notion of Articulatory Setting (AS) as a fundamental feature of a language, and one that teachers and learners must attend to if they are to get the best results. The PronSci materials have been shaped by the work that has been done on the English AS (and the related concept of Basis of Articulation).