The folks at DestroyerHistory.org sell a CD of engineering drawings of Bath Iron Works built Fletchers. These are scans of the drawings which were microfilmed. Their quality ranges from good to poor. The drawings cover items which are usually not modeled, piping runs, electrical wiring, internal tanks (fuel, sanitary, ballast), rivit schedules, and internal structures. It will get you closer (shapes/dimensions), but still won't get you to the details of the engine rooms. The major equipment (boilers, blowers, turbines, etc.) were built by other contractors and are referred in the plans only as numeric call-outs. You may only get a foundation drawing. [The same happens for most armament details].
Don't limit yourself only to the Laffey in your research. The National Park Service has the Cassin Young in Boston. In Buffalo there is The Sullivans, the Kidd is in Baton Rouge and the Joe Kennedy is in Fall River, MA. There is [was] a DE in Albany, NY and another DE in Galveston, TX. The Turner Joy [post Fletcher/Sumner/Gearing] is in Bremerton.
Contact the USArchives in Beltsville, MD. They have a room full of microfilm of drawings of all sorts of ship related items, including many of the Fletcher/Sumner/Gearing.