LOL!! I'm with you on those bands. Add Glenn Miller, Bob Crosby and the Bob-Cats, the Count Basie Orchestra, The Andrews Sisters, along with the Spike Jones Band. My mother was a Glenn Miller fan. I grew up listening to their music. We watched the Spike Jones show, and Kate Smith shows on TV. And Ernie Kovacs too. Great entertainment back then.
Never saw them, but our HS had Louie Belson, Clark Terry, Buddy Rich, Doc Severson, Urbie Green and a few others play with our Jazz Band. Not all at the same time :)