I don't have a tips or tricks for you, but quoting from their website:
How far in advance can I book minibar?
Reservations for minibar are taken a month in advance. That is to say, if you want a seat for the 15th of March, you would need to start calling on February 15. Please be advised that the demand for minibar by josé andrés is very high and seats are often booked up the day they are opened for reservation.
How do I make a reservation.
To reserve, please call Café Atlantico and minibar at (202) 393-0812. The reservation phone lines open at 10 am. Reservations are accepted on a first come, first serve basis. Please be advised that the demand for minibar by josé andrés is very high and seats are often booked up the day they are opened for reservation, often within the first fifteen minutes. For the greatest chance of success, we recommend calling as close to 10 am as possible. If you are unable to get through, or the date or time you are attempting to reserve is no longer available, we do keep a wait list and often are able to fill seats from off that list.