Stay
Start making your hotel reservations soon! 
It may also be a good idea to look for a condo to rent.
It is usually cheaper for large groups and each condo will sleep several people.
 
It may also be worth checking lodging availability in the nearby towns of Monticello, Green River, and Grand Junction. They are all within an hour to an hour and a half drive from Moab and may be able to offer more availability.
There are also several campgrounds, check discovermoab.com for availability.

Host Hotels