I had to change this slightly after learning that double-inanimate venns don't work, but the outcome is the same - one person accidentally hit the button too early. Venn machines apply their changes instantly, which kind of messes this idea up a little. Still, it sounds like fun. An alternative that might work better would be Venn chicken, the first person to hit the button doesn't get transformed, and the longer it goes the more likely you are to become something weird.

Note: When inside venn machines, you can't hear anything outside, so the whole counting down from outside the machine thing doesn't work. I accidentally loverlooked that detail when I was writing this.