Having the kids in school does not always make it easy to go on the less crowed times of the year. My family went from December 21st to 27th last year. We loved it so much that we are going again from the 21st to 29th this year and bringing the grand parents this time.
There are tricks, admittedly we have not been in the low seasons so I cant compare, but we did not find it overwhelming. Before we went I was very nervous, looking up kid leashed, family GPSs and ordering everyone the same colored T-shirt with their name on it. However when we got there it was no big deal, the trick is to Zig while everyone Zags, my kids were 2 and 6 and they LOVED it,
My biggest tip is this, eat breakfast in the room, get to the park early and take advantage of your morning magic hours. Head straight to Fantasy Land it will be pretty empty, go on rides. Go up through Mickeys Toontown fair, look through but dont bother waiting to see Mickey Mouse, take Walt Disney rail road back to main street get off eat at the Crystal Palace (call ahead and make reservations for about 1:00pm) and get your character fix. By the time you get out of the restaurant the streets will be packed, but that is ok because you have already done what you wanted to do, leave the park go back to the hotel and take a nap or swim whatever. At 6:00pm head back to the park when everyone else is tired and hungry and wanting to go home.