Those drills frequently took her south to the West Indies, most often to Vieques Island near Puerto Rico, where embarked United States Marines practiced amphibious landings.

The remainder of 1956 saw her periodically embarking Marines at Morehead City, North Carolina, and putting them ashore at Little Creek and at nearby Camp Pendleton.

Most often, her operations with the Sixth Fleet included visits to ports in Spain, France, Italy, Greece, and Turkey, and along the North African coast.

Such was her assignment in the fall of 1962 when American surveillance of Cuba uncovered the siting of offensive ballistic missiles on that island by the Soviet Union.

However, the Soviet Union withdrew the missiles and the tension abated, enabling Traverse County to resume her normal routine early in 1963.

She returned to supplying Caribbean bases and conducting amphibious exercises at Little Creek, at Onslow Beach, North Carolina, and at Vieques Island near Puerto Rico.

After transporting the 8th Marine Engineering Battalion from Morehead City, North Carolina, to Vieques Island, she arrived at Colon, Panama Canal Zone, on 12 March 1970.

She exited the shipyard on 11 June 1970, retransited the canal, and joined the Caribbean Amphibious Ready Group for a day before returning to Rodman Naval Station for further orders.

At that time, she was transferred to the Maritime Administration for layup in the National Defense Reserve Fleet at Suisun Bay, Benicia, California.