Ren Houbo writes to say that he is delighted with yesterday’s answers and examples, and is looking forward to hearing about handle. So here goes.
The l at the end of handle constitutes a syllable on its own, usually with no separate ə after the d. The word is pronounced ˈhænd.l̩. Being, therefore, ‘syllabic’, this l may be somewhat longer in duration than it would otherwise be.
When a syllabic consonant is followed by a ‘weak’ (unstressable) vowel, it may optionally lose its syllabicity and become the ordinary (nonsyllabic) equivalent. Thus in handling, with the weak-vowelled suffix -ing, the basic three syllables ˈhænd.l̩.ɪŋ are usually reduced to just two, ˈhænd.lɪŋ. (This is the process I refer to as ‘compression’.) In this compressed form, the l is indeed now at the beginning of a syllable. The same applies in handle it, ˈhænd.l̩.ɪt or ˈhænd.lɪt, where the compressed version sounds identical to hand lit. Note, though, that handle lit is different, ˈhænd.l̩.lɪt, with a syllable-final l followed by a syllable-initial l. Here, as always happens when a syllable-final fricative or liquid is followed by an identical syllable-initial consonant, the two consonants are articulated by simply prolonging the steady state, not by moving any articulator. (Compare the prolonged s in bus stop and the prolonged m in same man.)
As I see it, the only common cases in English in which a syllable-final consonant is moved into the following syllable are the intensifier at all ə.ˈtɔːl and the combinations it is ɪ.ˈtɪz and it isn’t ɪ.ˈtɪz.n̩t. These three expressions usually have a strongly aspirated t, which tells us that it must be syllable-initial. (Some people think that syllable transfer also happens in the case of linking or intrusive r in BrE. I disagree, because more ice mɔːr ˈaɪs sounds different from more rice mɔː ˈraɪs.)