Francis was selected in a democratic election by Cardinals the world over.  There should not be a plebiscite for electing the Pope, however parishioners should be able to elect a lay deacon to administer their parish (who, by the way, should be lay, not clergy - no celibacy) , with the parents electing the board of the school who would hire the principal.   Parish and school employees would be considered outside Hosanna Tabor and would likely be protected by Perry as it is currently being used to prohibit anti-gay discrimination.

Whether the local bishop assigns the pastor and associates or they are hired by the deacon administrator is an interesting question, but the administrator should be able to fire them for cause.  There should be a diocesan level administrator elected by the deacon administrators  with the bishops elected by the clergy.   If Rome keeps appointing bishops, it's property should be vulnerable in child sex abuse lawsuits.  Thy can't have it both ways.