I know almost nothing, but you should drop me a line anyway (that dance we both love @gmail.com). For one, I have nothing better to do, and now that you've planted the bug I am likely to spend the next week reading all about this stuff.
One suggestion is to reach out to some well-known jazz archives and ask for advice or contacts. Rutgers University, the National Jazz Museum in Harlem, etc. You could even try Joe Bussard, as long as you don't tell him you're into Swing Era stuff. Since it's only the process that matters, you can try classical collections, too.
In addition to Audition, Izotope RX Elements is probably worth a look. It's the consumer version of their professional thing, and it's only $29 (40 upside down $) right now (at least when I access the website from the US). Not sure whether they'll give you a download or try to charge you an arm and a leg to ship you a CD.