I found out you can look at their English song list here:
but unfortunately without the song numbers, so you can't write those out ahead of time. Sad.
I wonder if the list of Japanese songs is up somewhere... that would come in handy. Paging through the Japanese book there, I was able to find The Alfee and Pizzacato Five, but not Mari Iijima (飯島 真理), Utada Hikaru (宇多田 ヒカル), or Yasuhiro Abe (安部恭弘). I also tried some songs by title, but no Sunny Side Up or Ai Oboeteimasuka or Catch You Catch Me. I am starting to get used to the way Japanese titles are alphabetized at least. The Alphee is sounded out as "Za Arufii," and "Za" is just "Sa" with a marking on it, so it's under "Sa."
The karaoke system seemed to get annoyed at our singing or at my selection of "Sweet Transvestite" from "The Rocky Horror Picture Show," as it crashed when it got to that song. The staff was nice and fixed it, also extending our time a bit, and they brought us some free drinks to compensate. Oh right, I should mention they don't serve or allow alcohol... they brought us a Coke, a lemonade, and two waters.
Four of us for three hours cost $75 total, which isn't so bad split 4 ways. I recommend Gamba.