"Simpson" was designated on 1 December 1943 for conversion to a mode of fast transport, APD-27, but was replaced in January 1944 by , whose conversion was in turn cancelled. Resuming her convoy duties, "Simpson" escorted for over three months from 29 December 1943 to 9 April 1944 as she carried troops up and down the U.S. East Coast. During the remainder of 1944 and early 1945, "Simpson" escorted new heavy combatant ships on shakedown and training exercises along the U.S. East Coast. Among the ships she served were battleships and , cruiser , and carriers and .