[GeeTwo]

A possible compromise:
Distribute flyers announcing a paper airplane contest, possibly stuffing one in each program book or taking other pains to spread them widely but thinly. Use an unusual paper color. Encourage people to write their name and team number (or other contact information for non-team members) on the flyer, fold it into a plane, and launch it during a brief (2-5 minute) window during the buildup to Einstein. Have some sort of call out for the first person to hit the curtain, and perhaps a few other categories. Make it clear, both on the flyer and through announcements, that throwing paper airplanes (or other paper missiles) at other times or made of other materials is cause for expulsion.