Lesley Gore - "Maybe I Know" (1964)

Jeff Barry and Ellie Greenwich again.

Starts with the chorus (vocals on first downbeat, no intro). When you get to the first verse, though, it modulates to a different key. This construction sounds more like a bridge, really, but only for the first four bars. The second four bars are back in the home key, but it's not just a way of finishing the verse but instead this sudden back and forth between the tonic and IV chords that turns out to be as integral a moment to the song as the chorus, complete with harmony vocals.

Chorus, really, had moved from D minor to the relative major (F) and the end of the verse confirms this by landing on A major as a dominant chord leading back to D minor when the chorus starts again. Bridge does this, too. This song is full of gold.

Merle Haggard - "If We Make It Through December" (1973)

How was this song written? Did he just ignore the question of where he was at any given point and let the exposition go on over four sections, one minute and thirty-nine seconds, as it pleased to suit the poetry?

Because you seem to start with the chorus, but it evolves over four lines as though it were a verse. And then there's another one, with new words. Two choruses to start a song?

That would seem to be the case. The next section ("Got laid off down at the factory" etc.) is a verse proper. Notice how it uses the harmonic vocabulary of the part of the chorus that sounded like a verse!

This section has an extension that turns out to be a bridge. That's clever placement but perhaps cleverer still is the fact that it turns out NOT to be exploratory, quickly returning to the haunting progression you'll hear a couple more times when he repeats the two choruses.