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One of the best series of "big band" recreations were those done by Enoch Light and his "Light Brigade" for the "Project 3" label in the mid-60s (this was when stereo really came into being).  They are incredibly close to the originals (and in some cases, surpassing) and performed almost entirely by some of the greatest sidemen those bands had.  Here is a link detailing his man's recording history--curiously I always thought he was British until I read some of this.  Any of his "recreations" are worth looking for.

http://www.spaceagepop.com/light.htm