Puzzle solution/hints: A Choral Arrangement

In May I published a puzzle called A Choral Arrangement. No one ended up solving it without additional hints, and so none of the prizes were claimed! I admit that this was disappointing; I knew the puzzle was hard, but expected at least one person to solve it.

For those of you who worked on it but got stuck, here are a few hints, in white text, meant to be read in order.

Hint 1: Google around to see if you can figure out what’s going on with the text in the speech bubbles. If you’re having trouble, try googling in different ways.

Hint 2: Consider the words you got in the order they appear around the circle. Do you notice anything?

Hint 3: Hopefully you’ve now figured out an instruction from the replaced words. What numbers do you have at your disposal, for summing? If you have no idea, looking back at the flavor text might prove useful.

Hint 4: It’s natural to think of each ballad as being associated with the line between the speaker and the person they’re speaking about. The fact that there are dots next to each person means you probably need to draw the lines precisely. Once you do that, is there a natural thing to look at — perhaps where the lines cross? Remember: you still haven’t used the new words (the ones replacing the removed words).

And if you just want to take a look at the solution, click here!