Consider making CursorIterator more extensible. It would be reasonable to be able to subclass to provide a range iterator (i.e. a forward iterator that checks an upper bound key, or a reverse iterator checking a lower bound). Since the class is final and tryToComputeNext is private, this is not currently feasible.

Another minor point is that the state machine should probably include a CLOSED state (in which hasNext returns false, and repeated calls to close are idempotent).