The Endicott (DD495/DMS35) was a Livermore (or Gleaves) class destroyer. PitRoad made a set of Benson/Livermores in plastic 1:700 scale. Hasegawa is supposed to be coming out with a 1:350 scale plastic Benson/Livermore sometime soon.
In resin, Classic Warships used to make a 1:700 scale Benson/Livermore. Now OOP. Both Yankee Modelworks and Iron Shipwright make 1:350 scale Benson/Livermores.
Trying to model a specific ship during wartime is a difficult proposition. Ship's appearance changed at each yard period as armament & sensors changed. Here your personal research is critical. Benson/Livermores were similarly configured ships, often lumped into two subclasses. The key identifying feature between the two is the funnels. The Bensons had flat-sided funnels while the Livermores had round-sided funnels. Livermores were sometimes called Gleaves class.
The Endicott started life as a destroyer, but her mission was changed during the war to that of a high speed minesweeper (DMS). If you want to see what a DMS looks like, check the external shots of the ship at the end close of the movie 'The Caine Mutiny'. Ensign Willie Keith is acquitted of mutiny and rejoins a DMS, captained by his nemesis, his first skipper.