According to this description of the English phonotactics, the schwa /ə/ doesn't occur in stressed syllables. But Cambridge Dictionary Onlines, Oxford Advanced Learner's Dictionary and Longman Pronunciation Dictionary say otherwise: the word "because" has been variously transcribed as /bɪˈkəz/ or /bəˈkəz/. So in which source should I believe? Or is there any error in transcription going on here? Or is "because" the only exception? And are there others?
Learn English – /ə/ in a stressed syllable
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Given all your examples of supposedly rhyming words (they all rhyme for me a GenAmE speaker) having different possible pronunciations, both within a dictionary and between dictionaries, leads me to believe primarily not that there is some variation in pronunciation in the GenAmE population (though there very well may be variation (but consistent) between regional accents), but rather that these dictionaries are not scientifically consistent within themselves.
Either you have discovered an substantive inconsistency among these entries or these dictionary makers have performed research on all these pronunciation as part of their preparation but are not printing the outcomes/final results of the data leading them to make distinctions that are not meaningful for actual pronunciation or hearing.
You may want to construct a diplomatically worded letter to the editor in order to discover the reasoning for these pronunciations. I wonder if it would help to show one dictionary what the other dictionaries say?
"No English word can start with two stressed syllables" is just false, unless you define "stressed syllable" as "primary-stressed syllable", in which case it is trivially true (because by definition a word only contains one primary-stressed syllable).
A better rule is that no English word can start with two fully unstressed syllables (two syllables with a reduced vowel).
As you have found, it's definitely the case that an English word can start with two syllables with unreduced vowels. Some theories of English stress allow unstressed syllables to contain unreduced vowels (at least in some circumstances), while other theories of English stress treat any syllable with an unreduced vowel as having at least some degree of stress (theories may make use of a concept of secondary or even tertiary levels of stress).
Best Answer
I think the source of your confusion is that different people use different sets of symbols to represent the same pronunciations in English. Phonemic notation for English is fairly standardized, but it isn't absolutely uniform: for example, another area of variance is the notation of syllabic resonants (do we write the last syllables of button chasm bottle butter as /n̩ m̩ l̩ r̩/ or /ən əm əl ər/, or perhaps even /ᵊn ᵊm ᵊl ᵊr/?) and the notation of the "r" consonant sound (do we go with the simpler /r/ or the possibly more phonetically accurate /ɹ/?). In general, the difference between these is completely meaningless. Check the pronunciation guide of whatever resource you are using to learn what phonemic value some particular symbol represents.
When the schwa symbol <ə> is used in a stressed syllable, it almost certainly represents the STRUT vowel, even though this is standardly represented by /ʌ/. The "stressed schwa" notation for this vowel is probably most common in ad-hoc dictionary phonemic notation systems (I'd guess because it is more familiar to the general public than <ʌ>). Usually, notation systems that represent STRUT with <ə> will also represent NURSE with <ər>, <əɹ>, or <ɚ> (instead of <ɜr>, <ɜɹ>, or <ɝ>). It might not be entirely phonetically accurate, but neither is [ʌ] for many speakers (who may have a phonetic value more like [ɐ] or even [ə] instead).
This notation is possible without much, if any, ambiguity because schwa and STRUT are minimally contrastive at best, and actually in complementary distribution for many speakers. (See Accents of English by John C. Wells (who is also the author of the Longman Pronunciation Dictionary) for a description of this.)
The use of this notation in the Merriam-Webster dictionary was discussed at the following usingenglish.com forum thread: ə(unstressed) vs ʌ(stressed). The dictionaries you list evidently follow the same practice.
However, an earlier part of the Wikipedia article you referred to ("Vowels") defines the STRUT vowel as /ʌ/.
So the two sources simply use different definitions. The statement in the Wikipedia article is true, given the notation used there: it isn't true for all possible, or even for all existing phonetic notation systems used to transcribe English.
Note: I may be biased towards identifying /ə/ with /ʌ/ here because I do speak a dialect where "because" and "was" rhyme with "buzz," and "what" rhymes with "cut."
Peter Shor's explanation that it represents an unstressed weak form is also possible. It seems particularly likely for the Cambridge online dictionary; the evidence for it is that STRUT is usually represented by the symbol <ʌ> (I can't find any (other) word where /ə/ represents STRUT) , and for "but," they distinguish "strong /bʌt/ weak /bət/." The transcription in general doesn't always seem to be consistent; in the UK dictionary, "muzzle" is transcribed as /ˈmʌz.l̩/ but "guzzle" is transcribed as /ˈɡʌz.əl/.