I've used National at this location many times. National and
Alamo share their parent company and have a single service counter in the Guest Relations area off the Dolphin lobby. I've found the personnel to be friendly and efficient. You will go to the counter to start the rental. They will verify your driver's license and credit card info, hand you the paperwork, and give you the keys to take to the valet stand outside the front entrance of the hotel. The valet will bring the car around and you will be off and driving. On return, if the valet stand is open, give you keys to the valet and the valet will give you a receipt with the time, mileage, and fuel level noted. If valet stand is closed, use the dropbox. The valets are available much later than the closing time of the service counter (they may even be available 24/7), so you may not need to use a dropbox at the time of the return.
I've always received an emailed copy of the final receipt shortly after dropping off the car, but this has typically been during the day when the service counter was open. In any case, I would expect this to arrive soon after they open the following morning.