The only thing is, I noticed that you are dehumanizing the Trojans to make us like the Greeks better. As far as your edit goes, this is a good thing. But I just want to comment that this was the only aspect of the movie the original film-makers got right. In the "Iliad" the Trojans are protecting their home from an invading force and represent "good, old-fashioned values, protecting their families" (so to speak). The Greeks are meant to be shown as outsiders, in a murderous and impious light because they are later cursed. Agamemnon gets murdered by his wife on his return, among countless other stories taking place after the seige of Troy. Basically, showing the Greeks as "bad guys" was important because it was a morality play to teach others not to do those sorts of things in war.
But that's just a long tangent. I still think your edit will work well and will probably improve a horrendous movie. Cutting out cheesy lines will definitely be welcome. But if you want to keep the "Trojans as good guys stuff," then you will be retaining some of what was in the "Iliad."