With the Firenze Card, my reading of their website is that you can still access the Accademia even if all the time slots on the ticketing website are gone by choosing one of the following two methods below found their website FAQ:
www.firenzecard.it/en/faqs
I would love to have someone confirm that I am correct or incorrect in my interpretation as I am visiting Florence for only one day next October and may have a difficult time making a timed reservation due to transportation we are looking at the Firenze Card as well. To me it sounds like they have special time slots reserved for people who purchase the Firenze Card but i may well be wrong.
Here is the language from the Firenze Card website:
*Your Firenzecard includes entry to the Uffizi Gallery and the Accademia Gallery, as well as the reservation fee and any special exhibitions at no additional cost. For Firenzecard holders there are dedicated time slots, but you must reserve your entry time. Once you have a reservation, access the museum at the “priority access” door for reserved ticket holders. Note, you must reserve for each Firenzecard holder including any minors associated with the card.
Method 1: by phone
If you are not yet in Florence, we recommend that you book by phone and in advance calling the Firenze Musei call centre at +39 055 294883
• Operating hours for phone center: from 8:30am to 6:30 pm CET Monday to Friday; from 8:30am to 06:00pm CET on Saturday; from 09:00 to 06:00pm CET on Sunday and holidays.
• Choose your language, press 3 for bookings with Firenzecard and 1 to consent to data processing. Ignore any automatic messages that may indicate time slots not available.
• To book with the operator as a Firenzecard holder you must simply provide your first and last name. You will receive a reservation code that you must present at the ticket office along with your Firenzecard.
Method 2: in person
If you are already in Florence you can also book Uffizi and Accademia tickets in person when in Florence at the following booking offices by showing your Firenzecard or the purchase voucher. You can also transform phone bookings into physical tickets at these offices:
◦ Orsanmichele ticket office, inside the Church of Orsanmichele, entrance on Via dei Calzaiuoli (from 08:30am to 5:50pm from Monday to Saturday; on Sunday from 08:30am to 12:00pm);
◦ My Accademia ticket office, via Ricasoli n.105/red (from Tuesday to Sunday from 8:15am to 5:00pm, closed on Monday);
◦ Opera Your Preview , via Por Santa Maria 13R (every day from 10:00am to06:00pm).
You can buy Firenzecard and book and collect your Uffizi or Accademia entries also directly at the following museum ticket offices:
Galleria degli Uffizi ticket office (door n.2 only)
Museo Nazionale del Bargello ticket office
Palazzo Pitti ticket office.*