My first though on listening to the the middle part was that it sounds "classical," or at least "Broadway."

The first and third "Turkey in the Straw" parts are harmonized about as one would expect for tunes picked up from folk or "pop" performers, but the middle part sounds more like someone had a "professional score" to pull the harmonies (and modality) from. The obvious jump is that perhaps it's from a movie or broadway musical soundtrack. I did re-run my movie tape of Rogers & Hammerstein's Oklahoma movie version on the off chance it might be a "minor character theme" but it is obviously not derived from anything there.
Even "Turkey in the Straw" doesn't happen in that one.

The tune sounds "very familiar" but I can't figure out an Oklahoma association. It just isn't in a style that I can pin to anything that the local Okies brag about, or to any of the typical "folk" or "cowboy" traditions of the area.

I do seem to "hear" a similarity to some tunes/songs that I associate with a particular campground picker, so I've cut the middle part out and made a separate midi to play for him. Perhaps he'll be able to recognize it, or at least name a "style," genre, or era that it suggests. It will be at least a month, though, before I'll have a chance to try it out on him and get back.

It is an "intriguing" tune.

John