Asclepiades,
Although we may never know "for sure" the phonetics of Classical Latin, we have a pretty solid scholarly consensus regarding the matter. When it comes to actually utilising that information, though, to speak Latin, very few Classical scholars have put the time and effort into trying to speak Latin as they know it should have been spoken during, say, the time of the late Republic.
For example, regarding the AE phoneme, we know that in the early republic, it was pronounced as a full dipthong, "AI", and that after the republic, this became closer to simply a long "e".......KAISAR versus KEESAR.
We also know that in earlier times, the C was always a hard sound, as did the Greeks, later it altered according to its environment.
The amount of information we have to draw on for reconstructing the pronunciation of Latin is very large - and there is broad academic consensus as to how it ought to be pronounced . Where does the evidence come from? Latin words were transliterated into Greek, and also into Hebrew, with the words appearing in those languages as they sounded. We also have Latin rhyming verse from the 300's, and as we know it was supposed to rhyme, we can tell how all the final syllables were pronounced. Then there is the matter of the textual statements of the various Roman grammarians, who wrote extensively about how their language was pronounced. Finally, we have the large body of epigraphical evidence - the mis-spellings, the elisions - words written down as they sounded, not as they were 'spelled' ( to our way of thinking about it), which instruct us as to how the words were pronounced.
However, theory and practical application of theory are two different creatures, as I am discovering with my Latinum podcast. There are very few academics who are comfortable enough with the consistent accuracy of their Restored Pronunciation Latin, to want to record it for public exposure. I think this is because the focus in Academic circles, with the exception of a tiny minority of academics, has not been on vocalising the language. With my recordings on the Latinum podcast, I have my own recordings peer reviewed - and then I re-record the episode, until I am reasonably happy with it. However, even these are imperfect.
There are great rewards to getting it as 'right' as possible, as the Latin comes alive. The difficulties are compounded by the rules for accenting not being the same as the rules for syllable strength, (which applies in poetry and versification.) If you first encounter a word in a poem, the chances are that you'll not have encountered it used with its natural accent, and you'd in all liklihood mispronounce if you were to use it in speech.
Many people mix these up, ( I am still guilty of it from time to time) and use the vowel quantities when speaking, when they should be using the accents. To confuse matters even more, dictionaries usually only give the quantity, but not the accent. The rules for accenting spoken Latin are given by G.J. Adler on page 6 of "A Practical Grammar for Speaking and Writing Latin", where he says "correct pronunciation....is the very soul of living discourse".
Evan.