Later people read and understand older written material as well as spoken material. But the reverse doesn't work...a modern will understand the old because they know the spelling.
The first time that I heard Chaucer read aloud, I was surprised at how much easier it was for me to understand him when spoken. As far as I know, it's the custom of most modern editors not to modernize Chaucer's spelling. But I do understand your point about the inherent conservativism of writing and spelling in the face of language change.
Stress was preserved thoughout the ages and will be corrected today on the streets in Greece if and when a word is misaccented.
The pitch accent, which became a stress accent, is still present in modern Greek. However it was not a stress accent earlier than the first or second century A.D., where it begins to interfere with poetry. Before that period, the metre is carried entirely by vowel quantity, and accent does not interact with it at all, being entirely tonal.
For example, from Babrius, 2nd century AD, Syria:
Γενεὴ δικαίων ἦν τὸ πρῶτον ἀνθρώπων,
ὦ Βράγχε τέκνον, ἣν καλοῦσι χρυσείην,
μεθ᾿ ἣν γενέσθαι φασὶν ἀργυρῆν ἄλλην·
τρίτη δ᾿ ἀπ᾿ αὐτῶν ἐσμεν ἡ σιδηρείη.
Notice the paroxytone at the end of every line. That doesn't happen in classical poetry. The Seikilos epitaph (near Ephesus, dated from around the time of Christ) seems to respond to both vowel length and pitch accent in its melody. How did Paul's letter to the Ephesians sound when first read aloud to that congregation?
But the real question (for most of those on this board, I think) is whether vowel quantity was completely absent from the rhythm of natural speech across all the lands where the New Testament was written. All I can say is that Luke's Magnificat and Romans 1 both strike me as being strikingly aware of quantity. It's an aesthetic judgement, and I could well be wrong. I still know less about the papyrological evidence than I would like -- though I have read your paper, Horrocks, Allen, and others. To my understanding, while there is an abundance of evidence about the nature of vowel quality change, there is comparatively little evidence about quantity. Poetry is evidence, but it may all be pastiche like Nonnus, as you say.