John Wesley Harding has a few great songs in an alternative rock / folk kind of way. He was all early 90's for me, though he is still making music for purchase. He just kind of fell off my radar.
His second release - an EP in 1989 called G-d Made Me Do It - included a cover of a song that had been released that very same year...........by Madonna.
Harding covered "Like a Prayer" in an acoustic manner - and it works! The song is not done tongue in cheek, just straight forward.
Take a listen.