Steve,
USS Johnston was a square-bridge Fletcher whereas the Tamiya kit is of an early round-bridge Fletcher. It would ordinarily be better to start with the Trumpeter 1/350 USS The Sullivans, but there are detail problems with that kit. I know that Yankee Model Works used to make a Johnston in resin that was quite good. That would be the best route to go if you can find one.
That said, I recommend starting with the Trumpeter kit, improving upon it using the L'Arsenal detail set for this kit, and making the corrections necessary not covered by the detail set. This is the approach I am taking for my conversion to the USS Morrison (DD-560).
Bill Morrison