Evidence from the Romance languages provides fairly good evidence for distinct qualities, [ɛ] vs. [eː], for ĕ and ē in stressed syllables when followed by a consonant. Likewise for ŏ and ō as [ɔ] vs. [oː]. For ĭ vs. ī, the reflexes before a consonant are expected to be different not only in stressed syllables, but also in unstressed syllables for Western Romance (as *e vs. *i, reconstructed as going back to Latin [ɪ] vs. [iː]—although apparently there are some further complications in pre-tonic position for some languages, such as Italian, according to Unbrutual_Russian's comment on this Reddit post).
But before a vowel in unstressed syllables, ĕ and ĭ often develop to palatal glides or coalesce with the preceding consonant to form a palatal(ized) consonant. This has been interpreted as evidence that the short vowels ĕ ĭ ŭ may have had closer pronunciations [e i u] that were used before other vowels (vs. the opener [ɛ ɪ ʊ] that are supposed to have been used, in unstressed as well as in stressed syllables, before consonants). There is also some evidence related to the reflexes of prevocalic ĕ ĭ ŭ in stressed syllables, e.g. in disyllabic words like via or meus, but that seems a bit more complicated so I won't try to summarize it here. The pronunciation of words like that is not the subject of this question.
What I'm wondering about instead is what is thought to have been the quality of short ĕ ĭ ŏ in word-final position. (I'm not asking about ŭ because there don't seem to be any words where final -ŭ is firmly established; Cser 2016 says it could conceivably have occurred in the nom/acc sing of neuters ending in -u, but he presumes that these had -ū (p 127)).
I think that word-final short vowels occur in several phonological contexts: they might be phrase-final, or they might be followed by a consonant, or they might be followed by vowel. Elision was a definite possibility when a vowel followed, and it may even have been quite strongly favored (it was certainly frequent in poetry) but I have the impression that hiatus was not absolutely ruled out.
As a speaker of American English, I'm somewhat biased against word-final [ɛ ɪ ɔ]; [e i o] are more comfortable for me. My feelings have little relevance to the question of what Latin speakers did. But there are also other reasons why closer qualities for ĕ ĭ ŏ in word-final position seem plausible to me. As a rule, word-final i o are expected to be long. Final short ĭ ŏ seem to derive mainly from processes like brevis brevians and for some words, both a short and a long pronunciation exist (e.g. tibi, sibi, ibi, and too many words to list in -o). Final short ĕ is sometimes derived from ē (as in bene), but usually it isn't. However, it does often derive from lowering of word-final ĭ (e.g. in the nominative/accusative singular forms of i-stem neuters); it seems like this would necessarily have passed through a close-mid position [e] on the way to an open-mid position [ɛ], and I'm wondering whether we have any strong reasons for supposing that the vowel actually was lowered all the way to open-mid [ɛ].
I don't recall seeing a discussion of the quality of ĕ ĭ ŏ in this context in any grammars or pedagogical texts that I have read. Allen's Vox Latina doesn't seem to address it (which presumably means Allen would give word-final ĕ ĭ ŏ the pronunciations [ɛ ɪ ɔ]).
Evidence I've found for an opened quality for word-final ĭ
So far, my own research has uncovered the following piece of evidence for word-final ĭ having the quality [ɪ] rather than [i]: Italian has (d)ove from Latin (de) ubi. I don't find this especially convincing as evidence for the pronunciation of ĕ and ŏ, though, because it seems to me that high vowel phonemes might have behaved differently from mid vowel phonemes.
It could be somewhat indirect evidence against word-final ĕ being [e], in that if word-final ĭ and ĕ were [ɪ] and [e] respectively, they would be extremely similar in quality, and we might expect them to be conflated in spelling more often than they actually are (I don't actually know what the evidence from E vs. I spellings is, though: an e spelling does seem to be attested for ubi, but I'm not sure whether i spellings are attested for words ending in -ĕ).
So I guess ŏ is the vowel for which it seems most plausible to me that the quality would be closer in word-final position than in word-internal position.
For the purposes of this question, assume more than 5 vowel qualities existed
I know that some sources disagree with Allen's description and instead say that Classical Latin, or Latin in certain periods during/around the Classical era, had only 5 phonetic vowel qualities corresponding to the 5 phonemic vowel qualities (e.g. Andrea Calabrese's proposal of [ɑ ɛ i ɔ u], mentioned in the Reddit thread I linked to in the first paragraph). My question would obviously have a trivial answer in a 5-qualities system, so I'm only interested in answers that accept the hypothesis that we can meaningfully speak of more than 5 phonetic vowel qualities for Classical Latin vowels.