I have tried to get uncirculated bills from my bank, and was told that they couldn't guarantee the bills would be new. They would only give me what came out of their machine. I did only ask for 100, not 1000. When I asked them about getting uncirculated bills, the teller didn't know. She did ask her manager, but he didn't know either. He suggested trying the post office, since they sell uncirculated coins.
In terms of depositing the money back, what about depositing it in chunks? Say 100 or 200 bills at a time. Would that be a problem? I could easily make five deposits in an hour at five different banks in my area.
I would love to give this a try, but I am quite unsure how to really get started.