Strengthening American Nuclear Competitiveness Act This bill requires expedited consideration of certain nuclear technology exports, and it requires the Department of Energy (DOE) and the Government Accountability Office (GAO) to author specified reports. Specifically, DOE must establish procedures to expedite consideration of authorization requests regarding the transfer of a technology that involves specified low-proliferation-risk reactors to certain foreign countries. DOE must also report on U.S. civil nuclear commerce, including (1) an assessment of current practices with respect to the civilian nuclear industry and the impacts of such practices on both the industry and in foreign commerce, (2) a comparison of U.S. practices to the practices of foreign countries with respect to their own civilian nuclear industry, and (3) recommendations to improve the competitiveness of U.S. civil nuclear commerce. The GAO must report on the feasibility and implications of modifying or repealing specified restrictions on issuing licenses for certain nuclear facilities to an alien or an entity owned, controlled, or dominated by an alien, foreign corporation, or foreign government. The GAO must also report on actions by DOE with respect to the retrospective risk pooling program that requires each nuclear supplier to help cover the contingent cost resulting from certain nuclear incidents.