For purposes of preserving the integrity of the Official Map, no permit shall be issued for any building or structure in the bed of any street or public drainageway, flood control basin or public area reserved pursuant to §
160-108 of this chapter as shown on the Official Tax Map, or shown on a plat filed pursuant to this chapter before adoption of the Official Map, except as provided herein. Whenever one or more parcels of land upon which is located the bed of such mapped street or public drainageway, flood control basin or public area reserved pursuant to §
160-108 of this chapter cannot yield a reasonable return to the owner unless a building permit is granted, the Zoning Board of Adjustment may, in a specific case, by an affirmative vote of a majority of the full authorized membership of the Board, direct the issuance of a permit for a building or structure in the bed of such mapped street or public drainageway or flood control basin or public area reserved pursuant to §
160-108 of this chapter which will as little as practicable increase the cost of opening such street or tend to cause a minimum change of the Official Map, and the Board shall impose reasonable requirements as a condition of granting the permit so as to promote the health, morals, safety and general welfare of the public. The sections of this chapter that deal with appeals and applications, time for decision, modification on appeal and stay of proceedings by appeal shall apply to applications or appeals pursuant to this section.