For the complete leaderboard, see the link above. Our winner was
Six songs remained unguessed. They were:
4. I'm gonna stamp my feet until the policeman comes - Joe Jackson, "Rant and Rave" (BONUS POINT)
7. He'd just come along, scoop them under his arm like that - Crash Test Dummies (and covered by DC Simpson; I have both versions), "Superman's Song"
8. There's people there who'll hurt you because of who you are - Blur, "Coffee And TV"
12. And I knew it was time... to move on - William Shatner and Ben Folds, "In Love"
22. Feasting on bums that sleep in the park - Sifl and Olly, "The Panda Song" (BONUS POINT)
26. There's no cure, there's no answer - Joe Jackson, "Cancer"
With six songs left, three were the ones I'd marked obscure and therefore bonus-worthy. If I'd had a sixth point to spend (which I only didn't because five is a nice round number, and in accordance with the Law), it would have been on "Cancer", though honestly I have no idea how obscure an artist Joe Jackson is these days. I still hear him on the radio once in a while, and he was a guest artist on Shatner's new album "Has Been"...
Anyway. That's the way things turned out. I'll probably be doing another one of these next month when I'm absurdly bored again.