Heya, Chad; sorry about the constant invocation of Sanskrit; it’s pretty helpful, though, at times when it comes to Indo-European tongues. Neat websites. The first one, however, the “Latin Qvarter,” I am obliged immediately to disregard, for it definites the pronunciation of short i as being like the English word “it” or “is.” This low, relatively nonsonorous sound doesn’t even exist outside of English, much less in a Mediterranean language. Latin vowels, as we all know, are constant in their placement within the mouth, just as they are in Italian, Spanish, and many of the Romance tongues (in fact, in these languages, as well as Latin, the vowels are superior in influence over the consonants; this was demonstrated above where the vowels “e” and “i” actually force the velar consants forward in Vulgar Latin and the resultant Romance tongues, generating palatals and sibilants instead of velar stops). The English concept of “short” and “long” vowels comes from the vulgar, descended nature of our language; “A,” pronounced like the capital letter, is considered “long” because it is indeed a diphthong, spelled approximately in Latin as “ei.” “ah,” is considered a “short” vowel in English because it doesn’t take as much time to pronounce it. Likewise for the other four. But this unfortunate convention to which some stulti “Classicists” ascribe themselves is fundamentally flawed and inherently incorrect, and ignores the phonology and linguistics of practically all other languages.
The second website has more merrit, in my opinion; notice how the it defintes vowel length as just that, duration of sound. As for the nasal vowels that it maintains are what exist at the ends of these words, I believe I have found an answer which addresses that matter.
I certainly don’t mean to suppose these ideas are solely your own; surely your thoughts are well reasoned and supported. Nevertheless, from my perspective, I don’t see how these phonologists can possibly reconstruct the voces of these languages like this. Is there truly written documentation, by Cicero or one of his numerous contemporaries, which describes in detail the pronunciation of this favored lost language? Does the Greek have the same, perhaps hidden in one of the many volumes of Plato? This would be the only definitive proof against otherwise regarded linguistic intuition. I will gladly eat my words when Cicero describes to me the nasal vowels of Classical Latin accusative singulars in every position within a setence.
However, if there is lacking such a definitive description, then these reconstructive phonologists are, perhaps wisely, examining the eldest daughter of the many linguae of the parent Indo-European, id est Sanskrit. If these philologists are trusting Sanskrit (to a degree which they should not), then they would see how Sanskrit definitely does this “nasal vowel” thing for its accusatives, as I mentioned above — only when such an accusatively cased noun is followed by any other word that begins with a consonant. Indeed, on its own, a stand-alone accusative in Sanskrit — let us use the example of açvaha, horse, in accusative: açvam — we see that a true, distinct ‘m’ ends the word. This is how it is spelled in the devanagari; this is how it is pronounced. However, when the consonant of a following word comes after, such as açvam paçyaami, I see the horse, the true “m” appears to be lost, replaced instead with what in Sanskrit is called an anusvaara, a nasalization of the preceeding vowel. No stand-alone accusative ever has this sound in Sanskrit, because it wouldn’t make sense; the sandhi, as these sound-changes between words are called, only happen between words (and there are many different kinds other than this which applies to accusative singulars). Instead, this particular sandhi occurs as a direct result of being followed by another word.
In particular with this sandhi, as with all of them, it isn’t actually a change of pronunciation of the word. If one attempts to pronounce açvam paçyaami, without the deliberately changing to the nasalized vowel of the sandhi, at a moderate speaking pace, one finds very quickly that it is impossible to avoid making the sandhi. The anusvaara occurs naturally as a consequence of speech. That’s why it’s a part of the grammar of Sanskrit; because it’s already there when one tries to speak. The only difference is that the Vedics wrote out this sound change to make their written system one hundred percent phonetic. Sandhi are more familiar to us in a different form, when clitics are formed in Latin words. Archaic Latin cumservare became conservare, because it was easier to pronounce, because this pronunciation was a direct result of the compounded consonants involved. Another example of intraverbal spelling change is adfacio, which, over time, became “afficio.” The ‘d’ was absorbed into the ‘f’, and the ‘a’ loosed into an ‘i’. “Accipio” is quite the same.
For those of us familiar with French, we know that liaison, the linking of sounds of one word to the proximate ones, is absolutely essential to correct French pronunciation, and that we are forever doomed to be tourists in Gallic eyes if we fail to meet this requirement. This liaison occurs when one word which follows another begins with a vowel. Let’s look at an example: Est-ce que vous avez chanté? “Is it so that you have sung?” The main liaison is between “vous” and “avez.” Though when apart “vous” just sounds like “voo,” for its ending ‘s’ is dropped, when it comes before the vowel of a following word, in this case the ‘a’ of “avez,” the ‘s’ links to the ‘a’, making it sound as if the word is actually “vousavez.”
Now let’s return to Latin. Try saying, “amicum tenet suum,” as fluidly and naturally and speedily as a native speaker. Notice what happens? After several times, the final ‘m’ of “amicum” dissintigrates; the lips never quite all the way close. If they did, the words would sound too stilted in prosodical speech. Now, “equum meum videt.” After saying it fast a few times, you’ll notice that the ‘m’ of “equum” disappears, absorbed into the following ‘m’ of “meum.” However, if we say, “virtutem ita habeo,” no matter how quickly we say it, the final ‘m’ of “virtutem” remains quite the solid bilabial nasal that it is. In Sanskrit, the express phonological rule of pronunciation is that such finally 'm’s lose their closed perfection before most consonants of following words; but if the following word starts with a vowel, the ‘m’ is fully pronounced. The same seem to be identical with Latin. The only difference between the two appears to be that Sanskrit actually changes its spelling to accomodate the new pronunciation, and Latin does not. This conclusion allows all parties to remain consistant; the Romans retain their virtually phonetic spelling of the words, the reconstructors of ancient Classical phonologies can rest assured they are practically right, and the static endings of Latin accusative singular words are not of an improbable unbelievable pronunciation that doesn’t in anyway match its spelling. Everybody wins. 
