Maybe you don't believe me, since syllable lengths are so fungible in English. But it really does sound wrong in classical Greek. A good way to get a feel for this is to imagine saying English words while putting the emPHAsis on the wrong syllaBLE. Sometimes it's just a bit weird, sometimes it's totally wrong, and sometimes it actually turns into a different word. You wouldn't write a poem and try to fit the meter by asking readers to change which syllable in a word is emphasized. (Or at least, you would do so only rarely and for a specific reason.)
Now, in Greek, instead of emphasis, the relative length of vowels in syllables is prescribed and certain words are distinguished on this basis. In fact, whereas meter in English poetry is based on emphasized syllables, meter in classical Greek poetry is based on syllable length. So there is reason to think it wouldn't change just to fit a song melody. This is also why, though you can read Homer in English that is metrical, you can't get a feel for heroic verse without hearing it in the Greek.
Let me give an indirect example that shows why this kind of reasoning doesn't work across languages. In English, we often indicate sarcasm, emphasis, or a question by intonation. A heavy, slow word might be more important, or a word that is pronounced with the tone rising might indicate a question or uncertainty. This is because "a word" in English is the same word regardless of the tone with which it is said. But in Chinese, the "same" sound with different tones actually is a different word. So in Chinese, you can't indicate a question with tone, because that would actually make a different word. Instead, you have to move words around, so that to indicate a word is the highlight of a sentence you move it to the beginning, or to indicate which word you aren't certain about you move it to the end.
Human language is fascinating!