I think you can see that, while there are songs that simply don’t translate, there are others where at least the broad narrative is intact. You can see the short story possibility in the events detailed in Ode to Billie Joe and imagine rendering An Occurence at Owl Creek Bridge into song. They would lose the advantage the first has of repeated mention of the bridge in the chorus or of the shock denouement of the second if a mistimed turn of tune were to occur.

If writing a song called ‘Co-payment‘ you might want a different focus than a short story on the same subject. The song can cover more ground by doubling up on its meaning; a short story attempting this risks confusion. While short stories don’t need a big cast – I saw one consisting of a desperate text scribbled on a torn strip of wallpaper by a kidnap victim, so one first person narrative – there needs to be a protagonist and an account of what happens to them (or an allusion to same). Whereas a song on co-payments or the co-payment may expand on what it is, what effect it has, a short story will want an agent effecting co-payments or being affected by them.

I pay twice for good advice/For every prick is worth the price/Though sickened by this circumstance/It seems I have another chance

It appears there is enough here to start drawing character but, while that may be so, the sly double entendre of the second line is going to be hard to spell out in prose.