Title is better although I would drop the "Conventionalism is Dead" part.
So your position is that Society does not determine what is moral.
Forget the quotes at the top and make your case. Don't write like you're talking to jar.
You say that the idea that society determines what is moral was destroyed centuries ago by Socrates. Show how.
You're correct, you haven't done an adequate job with this argument. Your post is weak. You're arguing from the defensive position. Don't.
You're starting a topic, make your general argument for your position. Show the evidence or whatever supports your position.
You've been on this board long enough, start learning how to make a good presentation.
Sorry for being direct, but I'm short on time. Let me know when you need another review.