Ioway

Hmm...? I was trying to think if they ever rhymed "way" with anything, and I'll use it in a few moments.
Maybe it's just the sound. Io-way has a more rustic (hick!) sound than Io-wuh.
Also there's a phonetic sound that fits together: I-O-A (all hard vowels) vs I-O-uh.
Also think of the verse, "I owe Iowa more than I can ever pay, so I think I'll move to Californ-I-yay." There's your hard A rhyme. Plus again the rhythm of the sounds: I-O (owe) I-O-A (way.)
That's the only thing I could think of. As a lifelong midwesterner (Illinoy [no s sound!] and Indiana it was always pronounced "Iowuh" in my parts.

The more logical explanation is that the writers/producers/directors had nothing to do with Iowa but just wrote the film. As a native Iowan, hearing supposed "natives" sing Io-way just doesn't sound right. But it's a good film and every summer about state fair time, I wish I could steal away from New York City and see the butter cow and eat some good fair food.

The question of how to pronounce "Iowa" also comes up at the beginning of "The Music Man" when Professor Harold Hill arrives in River City, "Ioway" (as the train conductor says).

I-O Don't know...

Does anyone say Californiay? I'm a CA kid & can only remember people saying it tongue-in-cheek when trying to imitate a grizzled old 19th century prospector.