Where do you hear Childers' Appalachian roots most clearly, and where does the album feel furthest from that tradition?

Furthest is definitely Down Under, i feel his roots most on either Tomcat and The Dandy or Oneida

Yup. Down Under feels pretty far removed from the stories and sounds of the rest of the album. I thought Dirty Ought Trill was the closest to the appalachian tradition. The drum pattern definitely feels rooted in it. The lyricism paints a pretty clear picture of it. I kind of feels like album closes with Tyler heading back home.