When a metropolitan district is organized in only one county, the executive of the county shall appoint, with the advice and consent of the governing body of the county, a board of directors for the district consisting of three persons chosen from the residents of that county, except that if such county is a county of the first classification with a charter form of government and having a population of at least nine hundred thousand inhabitants, then no two such board members shall be residents of the same county council district of such county until one board member has been selected from each county council district. When a metropolitan district is organized in more than one county, the executive of each county shall, with the advice and consent of its governing body, appoint the number of board members allocated to such county as provided in section 67.1739, except that in a county of the first classification with a charter form of government and having a population of at least nine hundred thousand inhabitants, no two such board members shall be residents of the same county council district of such county until one board member has been selected from each county council district. In the event that the entities entitled to appoint the board members in such county are unable to amicably determine an allocation of such members to be appointed by each such entity, then the matter shall be submitted to binding arbitration in the same manner as provided in subdivision (2) of section 67.1739. Upon the petition of the executive of the county from which the board member received his or her appointment, the governing body of the county may remove any board member for misconduct or neglect of duties.