Contra dance has a very standard musical form: 64 beats in eight 8-beat phrases. Dances require this, though some only need 16-beat phrases and some work better if there's some 4-beat chunkiness. There are a small number of contra dances that don't fit this pattern [1] but I can only think of one [2] that's actually crooked [3]. Dancers certainly notice, which is not ideal as I don't want to make dancers think, but as long as the caller's on top of things it works. Playing around with "the walloping window blind" as a possible dance tune has me thinking how maybe if you could add some beats early in a phrase but still end it clearly, you might be able to keep people from having to think about it at all. The problem with the song in question is that (if A is the verse and B is the chorus) in the middle of the A2 and at the end of the B1 it adds two beats. [4] You can square it up simply by squishing the four rising notes into two beats instead of four, but I'm thinking you might only need to do that with the B part (where it's at the end) if you used the appropriate dance. Anything with a balance and swing in the A2, such as mary cay's, alligator reel, or heartbeat contra, ought to work.

Now I need to try this out with some dancers. I think it would work, but you can't tell until you try it. I also think there's some chance you could actually leave in both places where it's crooked, but I'm not sure.

[1] For example, the chestnut "money musk" which is only 48 beats or the modern dance "alternating corners" which takes 128.

[2] Cherokee Shuffle, when danced with the extra balance at the end gets another four beats of melody.

[3] A crooked tune is one that doesn't divide evenly into eight beat phrases.

[4] If you're looking at the lyrics the beats are added where the words are stretched out: "play-ai-ey-a", "crew-ai-ew-a".