What real-life Destroyer is Civ 5's modeled after?
Solution 1:
Actually, if you look here the in-game destroyer does have rear guns.
Looking over some of your suggested American designs, I noticed the numbering scheme used and searched Wikipedia for DD-443 (the number on the hull of the destroyer's icon), and came up with the Gleaves-class destroyer (specifically the USS Swanson)
Personally, I think they look rather close enough to call it a match.