I don't think you are really getting away from the Alpha Male Monkey model. Here's an alternate conversation that puts words in your mouth and might be true, or it might completely misrepresent you:
Bible Believer: "So... where is the Alpha Male Monkey in your model? Is it you? Why should I have to do what you say?"
Matt: "No no, there isn't one. Right and wrong are based on the suffering of the victim, not obedience to laws."
Bible Believer: "But that's just defining your moral laws as being equal to Utilitarianism. How do you know that's correct?"
Matt: "I believed the arguments of Utilitarian philosophers."
Bible Believer: "So they're the Alpha Male Monkeys?"
Matt: "No, I don't believe it because they said it. I believe it because I determined that it's true."
Bible Believer: "Then you are the Alpha Male Monkey. You are defining morality for all humans based on your intellectual powers. Why should I make you my Alpha Male Monkey?"
Not quite right
Bible Believer: "So... where is the Alpha Male Monkey in your model? Is it you? Why should I have to do what you say?"
Matt: "No no, there isn't one. Right and wrong are based on the suffering of the victim, not obedience to laws."
Bible Believer: "But that's just defining your moral laws as being equal to Utilitarianism. How do you know that's correct?"
Matt: "I believed the arguments of Utilitarian philosophers."
Bible Believer: "So they're the Alpha Male Monkeys?"
Matt: "No, I don't believe it because they said it. I believe it because I determined that it's true."
Bible Believer: "Then you are the Alpha Male Monkey. You are defining morality for all humans based on your intellectual powers. Why should I make you my Alpha Male Monkey?"