In his early days, Stewart did a lot of great covers: Dylan’s “Only A Hobo,” Mike d’Abo’s “Handbags and Gladrags,” Bobby Womack’s “It’s All Over Now” all come to mind, in addition to the excellent songs you mention.
Plus, the Faces did a cover of McCartney’s “Maybe I’m Amazed” that’s, well, amazing!
The Cardigans - Sabbath Bloody Sabbath, I don’t like it better than the original, but damn that’s an awesome re-working.
Dinosaur Jr. - Just Like Heaven. When asked why they did it, the answer was, “To get waver chicks.”
The Jazz Butcher - Roadrunner. Of course, it helps to cover one of the greatest songs ever, even if he universalized the lyrics a bit - “I’m in love with modern suburban bleakness.” Plus, Sikorskyes (spelling sure sounds correct) from hell!
And a cover song that I heard over and over again as a child, and made me the man I am today: The Fendermen - Mule Skinner Blues
“Hey Joe” Patti Smith
“Crimson and Clover”-Joan Jett and the Blackhearts
“Who Do You Love”-the Doors
“Captain Kidd”-Tempest
“Chinese Rocks”-Johnny Thunders and the Heartbreakers
“Sam Hall” Johnny Cash
“Viva Las Vegas”-the Dead Kennedys
“Red Temple Prayer-Two-Headed Dog”–Sister Double Happiness
“Jim Dandy” Black Oak Arkansas
“VooDoo Idol”-the Flesheaters
“Rumble”-Guitar Wolf
“Heroin”-Roky Erickson
“Diamonds and Rust”-Judas Priest
“Sally Go 'Round the Roses”-whichever version I love at the moment.
Which is also a single, featuring maybe the greatest all-time 7" art, and not just because of this, but also because of the flip-side, which is a Cheap Trick cover.