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I want to get in a point here about why Rawls sets up the original position and the veil of ignorance the way he does.

Rawls knows that the original position could be set up in lots of different ways. So is he being arbitrary? Hopefully not. After all, why should we care if his original position is simply the one he personally likes. There needs to be a reason for accepting his particular understanding of the original position.

Rawls believes that his version of the original position and the veil of ignorance are a proper setting for the choice of principles because 

there is one interpretation of the initial situation which best expresses the conditions that are widely thought reasonable to impose on the choice of principles yet which, at the same time, leads to a conception that characterizes our considered judgments in reflective equilibrum (sic). [Theory, section #20]

That's the reason that he believes we should accept his version of the original position. Rawls believes that it embodies ideas about making just and binding decisions that are deeply embedded in American culture. 

I think this has an interesting consequence. If I'm right here, Rawls is not trying to provide foundations for universal principles that apply to all rational beings. That would be the sort of thing that Immanuel Kant tried to do. On the contrary, I think Rawls is trying to start from the common ground of American culture and derive specific principles of justice. He's trying to formulate principles of justice for people in 20th-century America and in similar situations.