Well done, Little Jiiii-iim! Well done Little Jim </Neddy Seagoon>
That's close enough for me. Swing was the word I was looking for, as exampled by the following records:
Christina Aguillera - Candyman
Bette Midler - Boogie Woogie Bugle Boy (yes, first a hit for the Andrews Sisters)
More recently (and currently on playlists), Paloma Faith has released a song with a nod to tradjazz as well as swing, Upside Down,
Jive Bunny's first IIRC Number 1 was Swing The Mood, which was actually a cut'n'paste of samples of rock & roll tracks, but did use Glenn Miller's In The Mood as an intro and linking sample.