Bonjour, Rochelle! I grew up in a large family, but we never amounted to quite as large a group as yours! Luckily, my Moms Panel family is slightly larger and they had some quality intel to lend.
Since we're talking military,
Disney Mom Andi informed me that Shades of Green (ShadesofGreen.org) has facilities and resources to not only host the event but also to help plan your group's stay and activities at Walt Disney World too.
You could also choose to leverage the Grand Gathering planners, as suggested by
Disney Mom Jill. Just call 407-WDW-PLAN.
The Illuminations dessert party is a good time. I think something like a Hoop Dee Doo gathering would be even cooler. Plus, there's cornbread there.