It's *really* hard to find an album or song like that. "Hartford Stomp" is also a song title, so you get a bunch of false hits that way.
Do you know what year the track was recorded, what year the album you mention was released, what label the album was released on, etc.? If you have a link to either song or album online, in any form, that would also be helpful. Or, at the very least, where you heard of the existence of this track.
A quick look in discographies shows no recordings of "Plowin'" under Goodman's name, and only two under Barnet's, neither of which lists Goodman as part of the band. If you want to try to track those two down:
Broadcast, New York, January 27, 1941
Released on IAJRC 8 and Hep CD53.
and a later studio recording:
New York, 1942
Released on Blue Heaven BH7-702 and Circle CCD112.
So...despite all my "it's really hard to find" stuff, I do think I found what you're looking for. You might be disappointed, though, because it's Charlie Barnet without Goodman. Here's the IAJRC release mentioned above, with the 1941 date, and notice it has 1939 airchecks by Goodman on the A side:
https://www.discogs.com/Benny-Goodman-C ... se/8854223
If you still want it, here's the Hep CD that has the same Barnet date on it:
https://smile.amazon.com/Transcription- ... 000001MCC/
I am mighty impressed with myself. *pats self on back*