Reversing the polarity (or "phase") of one set of speakers on the dance floor will create very unsatisfactory sound on the dance floor, you will lose a lot of bass in particular. (Not something you want to lose in a dance establishment.)
So far one of the best ideas I've seen in this thread for "active" cancellation would be the ceiling speakers, placed above the dining tables spaced for slightly overlapping coverage.
Forget trying to cancel the bass (anything below say 100Hz or so) and focus on the midrange to high freqs. (250-15,000hz.) Use the following, fed from both channels of the DJ's mixer:
- stereo eq unit, 1/3 octave;
- audio delay processor, two channel;
- stereo amplifier of at least 350w RMS per channel.
Wire the ceiling speakers to the amp, observing proper series/parallel wiring to present no less than 4 ohms per channel, then connect each GROUP of speakers to the amp with the polarity reversed.
By playing with the eq, put full cut in all bands below 250hz; then adjust the others by ear to get the most cancellation effect at the tables.
Set the audio delays by ear, start with 3ms and go up (or possibly down) from there, again getting best cancellation.
This is a crude but fairly effective way to get the effect you desire without killing the sound quality on the dance floor.
PM me and I will get some info to you on specific equipment and a sample speaker hookup diagram.