I am afraid you are never going to get what you want. You basically have two choices: Listen to old recordings of great performers, or listen to modern performers trying to recapture the magic. Neither is perfect, and you must decide whether you care more about the quality of the performance or the quality of the recording. One of my favorites performers is Louis Armstrong. And my favorite period for him is the 1920's (not the big band you like). I have found a tolerable release on CD:
http://www.amazon.com/Hot-Fives-Sevens-Louis-Armstrong/dp/B00001ZWLP/
The best modern performers I have found of this sort of music is
The Federal Jazz Commission:
http://home.comcast.net/~fedjazz/index.htm
However, I have only heard them live, not on any of their CDs. They are well worth hearing, and their cornet player is great. But, of course, he is no Louis Armstrong.
One problem is that with recordings, one becomes spoiled, as one can hear the world's greatest performers, and often some of their greatest performances, so when one hears someone who is merely great (say, in the top 10 living performers of their type), one is naturally disappointed, as [usually] they are not the best person on a good day, and that is what one may listen to in a recording.
If I had never heard Louis Armstrong (and I have never heard him in person, and obviously never will now, since he is long dead), I would probably be perfectly satisfied with the cornet player in
The Federal Jazz Commission. But, unfortunately for him (and, in a way, for me, too), I have heard magnificent performances from the all-time world's greatest jazz cornet/trumpet player when he was in his prime. Who could possibly compete with that?