Off-season at WDW, IMHO would be
- January (after New Year's and avoiding the MLK federal holiday weekend)
- February - early in the month before President's Day
- May - pretty nice weather, Memorial Day weekend can be crowded
- June - early is better; late June brings the summer crowds
- August - after the 15th the crowds thin, but the weather is still steamy
- September, October - nice months to visit
- November - a nice time, but there are lots of events - Food & Wine Festival, Daytime Soaps weekend, etc.
- December - early in the month is a lovely time to visit and see the delightful decorations
With such a large group, you may wish to consider staying at a DVC resort. The largest of these resorts sleeps 12. They are pricier than a resort hotel, but you may be able to rent points from a member. At a DVC resort, you will have a washer/dryer, full kitchen area and lots of room. If that is not in your budget, you may want to try one of the moderate resorts. All are beautifully themed.
You also will be able to use Magical Express to get from the airport to your resort. This will save you a good deal, too.