I think if you are pretty sure that a group will do the Big Apple, pick a time when it would be nice for everyone else to take a break and watch (like after playing a couple of barn burners).
A couple of barn burners would clear the floor here (damn shame). Big Apple sucks to low-tempo, low-energy songs, so how does it help to keep it exclusive?
Not quite sure if I know what you are asking, but in a previous post you wanted suggestions on how to not kill the dance energy. My line of thinking was if there is a group you know would enjoy dancing to the Big Apple, and you know darn well Lionel Hampton's Flying Home will make them dance and everyone else watch, then try to pick a time when the other folks will be happy to sit around and watch.
In Seattle, playing a couple of fast songs in a row will keep most of the floor dancing, but the majority of the dancers can't dance fast all night. However, those that know the Big Apple well don't seem to get tired.....they would fully jump into it ever after some fast songs and everyone else could take a break and watch and be happy.
So I guess, depending on your crowd, I'd spin a Big Apple song after most of the floor has danced fully to the last couple of songs; i.e. it would suck to play a couple of other speciality songs (too fast or slow, etc.), then put on a Big Apple song.
I think encouraging folks to do dances like the Big Apple and the Shim Sham are good for the general lindy-hop community --- the more jazz footwork I learn the better dancer I am.
And the tap shim-sham is damn cool.