This is the weakest part of the argument. Why should anybody believe that there is a super complicated function that determines what is 'good'? ... Our brains come equipped with a simple function that maps "is" statements to "ought" statements. Thus, we can reason about "ought" statements just like we do with "is" statements

I think the claim isn't that there is a super-complicated function that determines what is 'good', but that the mapping from 'is' statements to 'ought' statements in the human brain is extremely complicated. If we claim that what is 'good' is what our brain considers is 'good', though, we merely encapsulate this complexity in a convenient black box.

That's not to say that it's not a solution, though: have you looked into desire utilitarianism? What you're proposing here is really similar to (as I understand it) that school of moral philosophy claims. If you have time, Fyfe's A Better Place is a good introduction.