>"The Toph Beifong Experience" would be a good name for a band.
>Presumably a loud one without much emphasis on big stage visuals.
If you want to check something out in that neighborhood, you should have a look at Boris. A Japanese three-piece (originally four-piece) that flirts with the outer fringes of doom, drone and psychedelia. Even their quiet music is played at ear-splitting volume, involving feedback textures and layers of guitar and other sounds.
https://www.youtube.com/watch?v=gop_ugTatAI (This video starts out pitch-black, but the lights do eventually come up.)
https://www.youtube.com/watch?v=DAr5VXXOGSQ (Official video for the two lead singles for the two albums they released simultaneously in 2011, "Hope" and "Riot Sugar." They cut back and forth between the two songs because they feel like it.)