https://www.radioechoes.com/?page=play_download&mode=play&dl_mp3folder=A&dl_file=afrs_v_disc_collection_194x-xx-xx_kay_kyser_and_his_orchestra_-_bye_bye_blues.mp3&dl_series=AFRS V Disc Collection&dl_title=Kay Kyser And His Orchestra - Bye Bye Blues&dl_date=194x.xx.xx&dl_size=479.6 KB
Sounds like White Glenn Miller to me...
Nope!
This guy was very "local". But his locality was large enough sustain him with a bit (or more) of good old-school hustling.
That, and being able to play his instrument quite nicely, as this sample hopefully attests to.
The tenor solo on The Chords record is by Dam The Man Taylor. I don't have any other data available right now, but the rhythm section certainly is in a jazz pocket.