In the future just leave the hotel and don't check out. The next day after housekeeping cleans your room, the front desk will check you out. Then just call for your folio to be faxed. I almost never check out at the front desk unless I need my folio right away. I've never had a problem doing it this way. Sometimes I'm just late leaving the hotel and don't bother to check out, or check out on the TV then leave the key in the room.
The early departure fee is if you leave and still have nights pending on your stay, not if you've already paid for that night. Call accounting at the hotel and they'll look at your folio and reverse the charge.
CF