People who live in areas under U.S. control that have never achieved statehood are part of the nation's commonwealth. They can elect local governments, but cannot be part of the federal government. There are provisions for people who have temporary residences outside of an established state. They can vote in their home state as long as they maintain a permanent residence there. People in the military, even when stationed overseas, can still vote in their home state's elections.
People living temporarily in D.C. as part of the government can vote back home.
If we amend the Constitution, it will result in a greater weakening of the principle of state sovereignty. That important principle has already been weakened by ever greater encroachments by the federal government. We need to return power to the states, not take more away. The District of Columbia was established as a seat for the federal government that would be entirely outside any of the several states. Our founding fathers felt, correctly, that if the capital of our nation were located within a state, that state would have an advantage over the other states.