The Military certainly does not want to start straining relations with some of the few living people left on the Island, and perhaps your idea of consolidating land does make more sense.
The Military therefore offers use of the Hospital, which is relatively close to the hub of buildings under Survivor control, in exchange for the Retirement Home, which is located directly between the Coast Guard and much of the (former) military installations.
In addition to this, the military will withdraw their forces from the area, and will not interfere with any territory south of the Coast Guard and west of the Docks.
Does this seem a reasonable solution?