I don't think you can go far wrong with any of the bands you mentioned,
but here are a few albums I know & like:

Andy Statman Klezmer Orchestra, Klezmer Suite
Klezmer Conseervatory Band, Yiddishe Renaissance
Kapelye, Future & Past (if this is not available on CD, try Levine and his Flying Machine)
Yale Strom, Cafe Jew Zoo (or Garden of Yidn)

Now you asked for American bands, but as good as the American bands are,
there's no reason to limit yourself to the USA.

Flying Bulgar Klezmer Band - that's the name of the band and the CD. They're Canadian.
Sukke, Introducing Sukke - they're European

Three Australian bands:

Klezmania, Oystralia
Spielazoi, Shtetl
KaOZ Klezmer, OY! KaOZ Klezmer Live

You may have trouble finding these last two. You might be able to reach Spielazoi
at spielazoi at iprimus dot com dot au, and KaOZ Klezmer at www.kaozklezmer.com
or fineyfarm at australia dot edu.