Somewhat unknown is John Fogerty's first solo album, put out under the pseudonym The Blue Ridge Rangers. The album fits the op's requirements in that Fogerty plays all the instruments and sings all the parts, but fails in regard to songwriting. The songs are all old Country and Bluegrass, done surprisingly (to me anyway) well.
Another such album is Dave Edmunds first solo (after disbanding Love Sculpture), entitled Rockpile (not to be confused with the sole album by the band he and Nick Lowe put together in 1980, Rockpile. Fantastic band and album entitled Seconds Of Pleasure). On the 1970 Rockpile album Dave performs (playing everything but bass, and singing almost all the vocals) old Rock 'n' Roll and Blues songs, utterly transforming "I Hear You Knocking" (written by Dave Bartholomew and originally recorded in 1955 by Smiley Lewis, with Bartholomew producing) from a Blues into a scorching Rock 'n Classic (with a killer guitar solo by Dave). The song was actually a hit on U.S radio, launching Edmund's solo career. One song on each LP side is a live recording, Dave backed by the group Brinsley Schwartz, of which Nick Lowe was at the time a member.