The Secretary of the Interior may, in his discretion, in addition to the extension authorized by section 333 of this title or other law existing prior to April 30, 1912, grant to any entryman under the desert-land laws a further extension of the time within which he is required to make final proof: Provided, That such entryman shall, by his corroborated affidavit filed in the land office of the district where such land is located, show to the satisfaction of the Secretary that because of unavoidable delay in the construction of irrigation works intended to convey water to the land embraced in his entry he is, without fault on his part, unable to make proof of the reclamation and cultivation of said lands as required by law within the time limited therefor; but such extension shall not be granted for a period of more than three years, and this section shall not affect contests initiated for a valid existing reason: Provided, That the total extension of the statutory period for making final proof that may be allowed in any one case under this section, and any other statutes existing prior to April 30, 1912, of either general or local application, shall be limited to six years in the aggregate.