The late Elliott Smith did covers of many Beatles songs, especially live (his exquisite note-for-note self-made cover of Because on the American Beauty soundtrack is amazing), but it is clear he identified most with George. His guitar-playing style was very reminiscent of 'the quiet Beatle', check out the shimmering solos on Bottle Up And Explode or Everybody Cares Everybody Understands or Can't Make A Sound and you will hear George somewhere in there.
But I thought I would share some live covers Elliott did of George's songs. The sound quality varies (being bootlegged from concerts) but all the performances are heartfelt. Check out:
Give Me Love (Give Me Peace On Earth) - http://www.radargrey.com/sweetadeline/G ... 0Earth.mp3
Isn't It A Pity - http://www.radargrey.com/sweetadeline/pity.mp3
and Long Long Long - http://www.radargrey.com/sweetadeline/longlonglong.mp3
He also did an awesome live version of I Me Mine. Among the many Beatles covers he did were Something, Rain, I'm Only Sleeping, I'm So Tired, Blackbird, For No One, an AWESOME poignant version of Jealous Guy, Yer Blues and Revolution.
I totally recommend Elliott if you haven't encountered his music before. All Beatles fans will instantly fall in love with his albums, for reasons which will become obvious after listening to albums such as XO, Figure 8 or Either/Or. Just sharing and spreading the word. Cheers.