Besides KW NAS, the USCG also has MWR housing in Marathon, MM 48.
Not sure of costs, but there are parks in the area at John Pennekamp Coral Reef State Park, MM 103, Long Key, MM 67 and Bahia Honda, MM 35.
BSA has a camp on Camp Sawyer, MM 33, Spanish Harbor Key, Big Pine Key, FL 33043
Also, The BSA Camp Ranger, 28400 SW 408 St., Homestead, FL 33034,, mite be a bit out of the way??
Good Luck..
Isn't Sea Base in the Islamorada area, MM 74??