I was in this show over 30 years ago in high school -- it probably was too dated, then, too, but it's so funny!  How about developing a good dramaturg to research all of the dated references so that the kids (and audience) can learn about the period and enjoy the humor?

I was AD on a production and the references are extremely dated.  But If you do the research and get the cast to have an understanding of the context it can be funny.   The idea is not so much for the audience to be able to have a reference for any of this but for the cast to be able to at least appear that they know what they're talking about.   As the saying goes "it's all in the timing."