You need a per user second rate (Calculated monthly), applied to the streams they actually listened to on a per second basis. Yes, it is a large calculation, but simple compared to most ML problems.
That would be 1 cent per 108 seconds, so listen to an 8m35 version of American Pie and Don McLean gets 4.75c. Listen to Heartbreak Hotel, 2m08, and Elvis gets 1.18c. Listen to a 1 hour podcast of "The Infinite Monkey Cage", and the BBC get 33.3 cents
If you listen 24/7, or 2,592,000 seconds a month, then your $10 means that Elvis gets a mere 0.05c
You calculation are bang on. Elvis getting a mere 0.05c seems fair in the case of this super user when the user needs a flat rate to consume and all the content providers need to be fairly compensated. If this doesn't seem fair then your issue is with the flat pricing per user per month. Which, without this, I'd bet the pie is much smaller.