Do you really want a refund or want to change to a different flight?
I don't have any experience with asking for a refund, but I have always had success in getting DL to change my flight (even airports) if there was a schedule change. Now granted, I am Platinum so I'm sure that helps -- but in general they are pretty accomodating.
You should call back with a reason why it doesn't work (i.e. cannot take that early flight because I have to meet someone or I have a nurse that comes to my house and draws my blood at 6am)...something to explain that it is a real burden rather than I just don't want to wake up early.
Would be very surprised if they don't help you