Ethics of writing another paper to be graded for use as a work sample
I guess you sound like you are trying to game the system and that your "graded assignment" isn't really the sort of thing that is expected. If you are trying to deceive, then, of course it is unethical. 

However, you might ask to submit a second writing sample along with the require one, stating that you think it represents your abilities better than your coursework. 

It would probably also be a mistake to ask your professor to participate in a deceit. But, his comments on a second sample would be fine as long as you are clear about the situation. 

Guard your honor.