I got discouraged with the web site, could never get the times I wanted.
I had my hotel manager get my reservations. I always stay at Hotel Aldobrandini (I did everything in email,web site, 39-055-211-866 phone) in Piaza Madonna in Florence. Ignacio, the owner, always gets our reservations and then we pay at the sites. Just give him the times and dates you would like plus a second choice. The B&B is in a former palazzo right at the beginning of the San Lorenzo Mkt ( and close to the Duomo) and only 3 blocks from the train station, simple, affordable and inc breakfast.
Enough on the hotel, we did the Accademia at one of the last ticket times so the crowds were gone and it was so nice to just sit back and look. The "Slaves" are just as marvelous to me as David and there is usually a special exhibit too. The Accademia can be small and magical,I spend all my time in two rooms.
The Uffizi did take about 3 hours, so we did it in the daytime, and had a late lunch befoe the Accademia.
If you already have your hotel or you do 3*, etc, have the manager get your reservations; definitely the easiest way.
fyi..I wish I had rented the audio tape or even joined a tour, the Uffizzi has magnificent art and statuary. It was a little crowded even in Sept, I can't imagine summer. Go early and do something else in the middle of the day, so much to see in Florence