This is interesting. It's a very common problem evidently. And it's another reason for the increasing number of Arranger-type pianos in churchs. With something like a Clavinova, or a true arranger, the keyboard player controls the drums. An added advantage is that ALL parts can be sequenced ahead of time in case one or more band members can't be present every time. The drummer can then be in charge of passing the collection plate. He can use a tamborine.
Please forgive me, I know not what I say.
DonM