You should check out Sammy Hagar’s version of this song. I’m thinking it’s what you imagined for Axl. Sammy recorded this over 20 years ago.
It may have seemed like a joke, but I really would like to see someone – anyone – cover King Missile’s “Martin Scorsese”, but rename it “Quentin Tarantino”.
I’ld like to see M. Ward run with his cover of Let’s Dance and do a whole album of 80’s covers.
Todd Snider do a cover of Aaron Neville’s “I Don’t Know Much”
I’d like to hear a female fronted band/female vocalist do a cover of “The Letter” by The Box Tops, changing “she” to “he” as appropriate. Cat Power, Sons & Daughters, or Nouvelle Vague would all be interesting possibilities.
I’d like to hear Tiger Baby or Sally Shapiro cover “Freedom Hangs Like Heaven” by Iron & Wine. I can sing it, and it’d be nice to hear a girl with a sweet kind of fragile voice take a crack at it.
I’d like to hear “I Met A Girl” by Wheat covered by Pete Yorn.
I’ve always wanted Clint Black to cover the hits of Hank Williams Sr.
Off the Beat or Purple Haze on Champagne Supernova.
Don Henley wrote a terrific barroom song called You’re Not Drinkin’ Enough. It’s a shame it hasn’t been covered by Dwight Yoakim, Alan Jackson, or somebody like that. BR-549, maybe. 
Bare Naked Ladies - Frank’s 2000" TV
Willie Nelson, Faraway Eyes.
OK, work with me here.
I think Aerosmith could have (maybe still could) cover “Runaround Sue.” I can hear Steven Tyler’s trademark scream as he sings, “she goes…OUT WITH OTHER GUYS!”
My cover wishes are more generic. Basically I’d love to hear covers of all of my favorite songs:
I love covers that change the genre of the song. I seem to especially dig punk covers of non punk songs, mellow renditions of high energy songs, and offbeat covers like toy piano, acapella, etc. I also like rocking versions of classical melodies.
I’d love to hear English versions of all my favorite Spanish songs and Spanish versions of all my favorite English songs. Actually, I love to hear covers of any of my favs in any language. I wonder what normal songs (i.e. not birthday or christmas or church) have been most translated.
I’d also love to hear covers of songs by or of some of my more obscure fav artists like Indigo Girls, Dar Williams, Jill Sobule, and Ahmond.
Especially cool would be collaborations by 2 or more of my favorite artists on their own songs.
I wish Stewart Copeland would do a cover of any Paul Simon song he wishes.
Just the other day, to keep the bears away, I was singing what I think a Johnny Cash cover of ‘Wild and Untamed Thing’ from the Rocky Horror Show would sound like.