Rhyming with “symbiosis” would be consistent with English pronunciation, derived from Latin stress rules. Placing the English stress on the ancient pitch accent is truly a modern Greek habit, not one that we have inherited through the classical tongues. For the word to be stressed “apoptosis,” then it would also have to be symbIosis, an illogical choice that would not convene.
kilo/metre baro/metre hygro/metre etc.
(Kilo/metre is now often pronounced as ki/lometre.)
I doesn’t look like logic has much to do with it.
From what I understand of the way syllables were divided for poetry, it would seem that the word would be divided a.pop.to.sis in pronunciation. On the other hand, ancient practice would syllabify the word as a.po.pto.sis. My feeling, though, that this was just a writing convention (based on what group of consonants could start a word), and that the poetic practice better reflects the actual pronunciation than ancient theories (because any syllabification amounts to a theory of how to syllabify words), but in the end I’m not sure about that.
About the vowels in the word, I’m not sure how to describe them, because I’m in the odd position that my English dialect doesn’t have good equivalents of the vowels that occur in the Greek word - and then there’s the problem that I don’t even know if my ‘pop’ sounds like your ‘pop’ (mine has the same vowel as the ‘a’ in ‘father’). (If you’re familiar with the IPA, though, the pronunciation would’ve been something like [apoptɔ:sis].)
And then of course, the classical pronunciation would not have stressed any of the syllables but the first ‘o’ would’ve been on a higher pitch than the other vowels. But I think it’s an interesting question of which syllable an modern English speaker would hear as stressed, because they wouldn’t necessarily associate that higher pitch with (their imagined) stress – but I don’t think we’ll ever know the answer to this because we don’t know all the details about the prosody of Classical Greek.
2. What would be the best English pronunciation for this word? > (Obviously this question is a little more subjective than the first).
My first instinct is to stress the TO, because of so many other words so I’d go with that (although there are some words like ‘apotheosis,’ where the OED says the “great majority of orthoepists” say the stress should be on the ‘e’, and I’m not a big fan of filtering Ancient Greek through Latin especially in cases like this where the word comes directly from the Greek). But I don’t see the reason for not pronouncing the second ‘p’ or for a long ‘a’. So I’d say something like a-pop-TO-sis, with the a-po like ‘apoplectic’, and the TO-sis like ‘ptosis’.
But now the anti-prescriptivist in me has to say that I think the best pronunciation is the one that wins out in the end 
.
But I though that the Romans did identify their accent with the Greek accent in terms of phonetics – isn’t that what causes the whole debate of whether Latin had a stress or pitch accent? Plus, the fact that the accent of borrowed words was assimilated to Latin phonology is what you’d expect (just like when English borrowed words like ‘colour’ from French, it accented them on a different syllable than the French), so you can’t conclude that Latin speakers didn’t hear the high pitch as stress. And in the end, with English and Latin being different languages, why should how Latin speakers react to the Greek pitch accent tell you anything about how an English speaker would react?
A Roman would stress the pænult if long — thus we would as well — as in this word.
Why “thus?” Why should English speakers today consider what speakers of another language did two thousand years ago?
I think the modern pronounciation simply depends on where you are from. I was taught to say a-pop-toe-sis but I was also taught to say sym-bye-o-sis. Might just be my Canadian accent, though.
As for:
kilo/metre baro/metre hygro/metre etc
I was taught to say kil-o-me-tur and bar-rom-me-tur, however, I have no idea what a hygrometer is, so I can’t say how I would say that.
They seem to have to have gone a lot further than that, what with distinguishing between acute and circumflex accents and so on. It seems to me, that whatever their reasons and whether they were right or wrong, Roman grammarians applied the terminology of the Greek pitch accent system to their stress accent (if stress accent it was), and not to other variations of pitch – and that suggests to me they did consider the Greek pitch accent to be equivalent to their stress accent.
The Romans perforce would have stressed the long pænultimate when Latinizing the noun. The Greek pitch accent was fixed. The Latin stress was fixed — however, the Latin pitch accent was > not > fixed; as in Italian and Spanish and others, the variations of pitch are mobile, while the stress (volume) is rather immobile. Although Latin pitch accent would tend to fall on the stress, it did not have to.
But it seems to me your conflating two distinct phenomena: pitch accent and intonation, both of which might involve variations of pitch (although as you say, stress can do the same) but they’re still distinct. Ancient Greek would have had both, but it’s a shame we’ll never know what the intonation of Ancient Greek was and how it interacted with the pitch accent (except with question words or before pauses as you point out). Although, I’m not sure what you’re trying to say here.
Isn’t that the subject? How to pronounce the Greek word in English? a quæstion which necessitates analogy to the past. The reason is that Greek words are invariably tempered by the Latin medium even if neologistic in our language, through spelling as well as pronunciation. Greek words with υ are translitterated with ‘y’, and ου becomes ‘u’; κ becomes ‘c’, and we write ‘ph’ for φ (“catastrophy”) based entirely on the Latin model, and not the Modern Greek one, or an imaginary English one. Some 36,000 words of ours are Greek, and they operate in a logical and cohærent manner.
I wonder if it’s not the case that the English pronunciation of Greek words is more influenced by French than by Latin, and if this were true does it mean we should follow French practice, which regularly ignores Latin stress? The best thing seems to me to be to work directly with the (Ancient) Greek and assimilate Greek words directly to English instead of through some other intermediary.
Whose accentual properties neatly coincide with the stresses — most of the time.
But it seems to me your conflating two distinct phenomena
I conflate nothing. Exsufflicate perhaps, but conflate never.
The afforementioned “public” example stuck out in my mind after a recent viewing of the Star Trek: Voyager episode “Scientific Method,” and in the following scene B’Elanna and Tom discuss how public they wish their relationship to be:
http://robertranieri.com/voyager_pitchaccent.mov
You’ll see that at the end of the clause, she causes the final syllable to rise in “public” — an accute accent by Ancient Greek definition, while the stress (volume) is on “pub-.” Before that, she says “agreed” — the pitch accent coincides here with the stress, on the “-reed” part — this pitch accent is circumflex, a quick rise and fall on a long syllable. These specificities are difficult to tease out at first, especially with the abuse of the terms by French, Italian, Spanish, and others, but the Ancient Greek system is quite clearly defined.
Also, notice how there is an accute accent on “wéll,” right before a pause. And there are other notable features in this dialog. While these pitch accents are not hard fixed rules in our language, which is stress based, they were fixed and regular in Greek. Listen to others around you; you may find that there is much more music going on than you once noticed.
Lucus,
Isn’t “exsufflicate” an adjective?
Cordially,
Paul
And just what part of this invented word of Shakespeare’s should exclude it from being a verb, my friend?
It’s a perfectly cromulent word.
Heck, I don’t know. I just looked it up at dictionary.com and they said it was an adjective! 
“To make empty or frivolous?”
Cordially,
Paul
“To say nonsense,” I thought.