The governor and council, upon petition and upon the recommendation of the department, may, for just consideration, grant to an owner of a shoreline on public waters the right to excavate, remove, or dredge any bank, flat, marsh, swamp or lake bed before the owner’s shoreline. Every petition to excavate or dredge said areas shall be filed with the department. The department, after 30 days’ notice to abutters and within 60 days of receipt of a petition, the local governing body of the municipality in which the property is situate, and the department of health and human services shall hold a public hearing. Notice of the hearing shall be published twice in 2 different weeks, the last publication to be 7 days before the hearing, in one newspaper of general circulation throughout the state and another newspaper of general circulation in the municipality. The notice shall also be posted in 2 public places in the municipality. Upon appropriate investigation and within 30 days of a public hearing, the department shall make its recommendations to the governor and council with regard to such petition. If the department recommends that the petition be granted, in whole or in part, such recommendation shall include appropriate specifications and conditions necessary to the protection of public rights and to the protection of the rights and privileges of persons owning land in the vicinity of the area to be excavated or dredged by the petitioner.