Hi Greg - I read the same book, and had the same idea. I've always been interested in WWII destroyers, the "Greyhounds of the sea" as they were called. I'm doing research to begin building the USS Johnston, DD-557 from the Tamiya kit. You can check ship numbers on the Taffy 3 site someone else mentioned. Here's a photo index site:
http://www.navsource.org/archives/05idx.htm
and a good reference site on the Fletcher class:
http://www.destroyerhistory.org/fletcherclass/index.html
You may find, as I did, that the boat you want to build is a later Fletcher version, with the "square" bridge as opposed to the early "round" bridge included in the Tamiya model. I found a resin conversion kit at Tom's Modelworks (it's online) though I don't know if he has any more of those kits available - I think I got one of his last few. Good luck.
On the bench:
Not much right now, just getting started again.