Also, note that double hits happen more frequently when you hit the cymbal hard. Go into Rock Band 2 and into Drum Training/Freestyle Mode (I forget exactly what it's called, but it's the mode where you can play the drums freely). RB3 does not have this mode. It's easy to see the double-hits in there, so you can diagnose which of your cymbals is busted.
Sorry I couldn't keep up the shouting, but my virtual voice was getting hoarse.