The example you cite is not only ethical but normal in American non-profits. It's how many of us keep good things going! Many (possibly most) 501(c)3 boards are "self perpetuating" via governance nominating committees not only in museums but in other areas. First-hand examples I'm familiar with, include social service agencies, universities, neighborhood associations, alumni organizations, travel and tourism councils, historic preservation agencies &c. Often, other non-profits actually officially sponsor the creation of new non-profits which, in turn, become self-sustaining through common communities of interest. With roots in de Tocqueville's observations, we've long used this mechanism as the ways and means to get good things done in a democratic society. Pretty empowering stuff! Disclaimer: as empowering as this system can be, politics and personal agendas often upset the opportunity afforded by this sytem! In any case, good luck to you.