The only possible answer I've read on who does the litter kills theme song, is Bill Lawrence's wife and the shows' Cleo, Christa Miller. It kinda sounds like her, but I'm not convinced yet.
"As far as who sang the Episode 10 version of the theme song, it was a woman we hired through Mad City to sound like Sarah McLachlan"... "and can't remember her name. But it is sadly not Christa Miller. Christa was very shy to sing in our rock opera, but she did a great job once we finally convinced her to do it."