> so in (ancient) Greek, were there words which were the same as each other but for syllable length?
Yes, of course. I know very little classical greek, but here's an example from Latin:
malum - adjective, "bad"
maalum - noun, "apple" (I've written the long 'a' as two 'a's, which is not normal practice).
Contrastive vowel length is a very normal language feature; consider modern Japanese.
> I wanted to double check on this belief, and thought about it while listening to Elton John's "I'm Still Standing" (which was already playing) and Stanford's Magnificat in G to add a different genre, in both cases the emphasis is often on different syllables to how we would speak it if we just saw the text without knowing the music.
Modern songs and (especially) poetry vary in quality in how well the natural rhythm of their language fits the rhythm they're set to (there's no particular reason to believe that this only occurs in the modern day). It's definitely true that there's a lot of material that doesn't do that well, but I personally find that sort of thing jarring, and ovrwhelmingly the rhythm of the language and the rhythm of the piece are compatible. Given a large enough corpus, it's quite possible to figure out what rhythm(s) a word really wants to have.
Finally, remember how I said that marking vowel length in writing was not normal practice at the time? You might be interested to know that we know the vowel lengths in Latin words from their use in poetry.
Fun side note -- there's a famous Latin poet called Ovid; his name in Latin is Ovidius (four syllables: O-vi-di-us). All of those vowels are short. The last syllable is easily malleable, as it's a case ending, but the fact that the three syllables before it are all short means that Ovid is always referred to in poetry by a nickname, since Latin poetry essentially never allows for three short syllables in a row.