I'm not very familiar with the Better Yet podcast, but they recently came to my attention when they put together all of god's money / a tribute to wilco's yankee hotel foxtrot. It's a track by track covers album, obviously for Wilco's beyond classic album. Each track is done by a different artist, and the one that got our attention is Laura Stevenson covering "Jesus, Etc." Stevenson's version is a slightly slower, more symphonic version. It's a gorgeous song, and the perfect type of cover that stays true to the original while still sounding just like Laura Stevenson.
You can listen to Laura Stevenson's cover of "Jesus, Etc." below. all of god's money / a tribute to wilco's yankee hotel foxtrot below. The album is available via Better Yet's Bandcamp. For more on Laura Stevenson, check out her website.