My first thought when I read this was that I recall Pete Rugolo doing a chart that featured a tuba.  I'll pull out the CDs and LPs and check.  Also, I don't know where you would find it, but the recording of Night Train on Maynard's Blues Roar, while it does not feature a tuba solo, has a prominent role for a tubist (or, is that tubaist? idk) in the melody.

Check out this site: http://www.mjtproject.com/aboutmjt.html  I came across their version of My Favorite Things a while back.  It's not a traditional big band, but it sounds cool.

And, finally, try this link for some info on jazz tuba CDs:  http://www.dwerden.com/tuba_cd.cfm#Jazz

Now, I'm off to listen to some Rugolo...