Another song made for the movie but much less well-known: Gathering Storm. Also originally sung by Hazel Dickens, it was written by Mason Daring for the movie. Less obviously topical, but I suppose relevant.

The only recording of Hazel singing the song I could find was a very low-quality recording posted to Facebook which seemed to be a phone recording of a TV screen, so instead I'll share Mason's singing of it.

https://www.youtube.com/watch?v=KZn7LrTMQvU

Other songs I found:
- The Matewan Massacre by Hammertowne
- Coal Black Miner Blues by Nimrod Workman
- Bloody Mingo by Jay Clark
- Battle of Blair Mountain by David Rovics or Louise Mosrie
- Blair Mountain by Great American Taxi

Most of these aren't really "authentic" folk songs, but many are very real and intentional songs about the events.