I listened again to this and I really think it's Tommy Dorsey in a Jack Teagarden mode; when he starts playing the double time notes in his solo. I'm sure TD had heard him [and prob. wasn't too happy Teagarden was in NY !] The trombone solo starts out with the vibrato and sound that Dorsey was known for. The rough notes we hear could be Dorsey a little tired, maybe hung over [he was known to tip a few back].
Another note: I seem to recall a few recording sessions with Hoagy and Tommy both present [going back to the Gennett sides]..prob. a good friendship, too ! that's my 2 cents !