In those cases where an amendment to a zoning map is requested by a property owner for a specific use of property which is not permitted in the zoning district where the property is located, but which use would not substantially conflict with the permitted uses in the zoning district, the Legislature, in lieu of an amendment to the zoning map, may grant a variance for that specific use of the subject property; provided, however, that all other requirements of that zoning district will continue to apply to the subject property.