Success! I have reservations for the Uffizi, the Accademia and the Pitti Palace. For all who are interested, here's the info:
Call between 8.30 am and 6.30 pm Mon-Fri or Sat 8.30-12.30.
011-39-055-294-883, then #2 for English, #4 for reservations. You can reserve for all the museums in one call and will get reservation numbers for each visit. I was on hold for about 4-5 minutes, but then I spoke with a very nice, helpful woman.
The reservation fee is 3 Euro per ticket. You pay when you buy the tickets. Remember, when you get to the museum, if the ticket line is short, skip the reservation and save the money.
Currently tickets for the Uffizi and the Accademia are 10 Euro each (not 6) because there are special exhibitions.
You can also book on-line, the fee is 4 Euro per ticket. It looks like there are many fewer time slots available than by phone.