I am sometimes still confused when it comes to weak vowels. Today [in LPD] I found ʊ in spatula and u in occupy, although they seem equal and appear in the same environment. I also noted that they are replaced by the same symbol in the transcription of the American-English pronunciation - ə.Actually, it’s not true that they “appear in the same environment”. A crucial difference is that spatula has a weak final vowel (ə), while occupy has a strong one (aɪ). Consequently by my syllabification rules (which you may disagree with) the second syllable in spatula is closed, while that in occupy is open: the l of spatula remains in the default coda position, while the p of occupy is captured into the final syllable by the following strong vowel.
My introspection and observation leads me to think that in RP, or at least for me personally, we typically have a vowel ranging over [ʊ ~ ə] in a closed syllable but over the more firmly back [u ~ ʊ] in an open syllable.
Compare stimulus and stimulate, which I have transcribed ˈstɪm jʊl əs and ˈstɪm ju leɪt respectively (in each case also with -jə- as an alternative possibility).
In American English, yes, -jə- would be normal; but in BrE, for someone of my age group, my reaction to it is that that would sound uncultivated or at least very casual.
You may think that I have made things unnecessarily complicated here. There is obviously a gradual tendency for the British to follow the Americans towards generalizing -jə- in these weak syllables. But we haven’t by any means got there yet.
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If you would like to see and hear me chatting about teaching pronunciation, here are two television interviews recorded when I was in Argentina recently. They are in programmes 25 and 26, but you’ll have to wait for 15-16 minutes of other material first each time.