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I, too, have had Farhad Manjoo's problem: too much music, too little time. My iPod, too, suffered from having the same tracks repeated ad nauseum. So I came up with a solution - it's clunky, but it works for me.
1) I delete all songs from previously played albums off my "Party Shuffle" list.
2) I move 10 albums whose songs are listed on my slimmed-down Party Shuffle into a special folder.
3) Whenever I crave music, I turn to that folder first.
4) Rinse, repeat.
Voila! My backlist of unplayed music is rapidly dropping.
You, too, can do this.