So instead the three of us went to, where else, Luna Park. Where we were seated at the same three-quarters booth that we've been seated at the last five or six times we've gone there. (We've gotten pretty good at showing up during off-peak times when there are booths free.)
So at Luna Park when it's your birthday they bring out a giant cake with a candle and a _huge_ sparkler on top. After the sparkler dies out they let you blow out the single candle, and then they take the giant (fake) cake away and replace it with whatever dessert you actually ordered.