It sounds like you're looking for excuses. You said you are involved in your church. My experience with church is that couples whose marriages work take time for each other. Are there no other couples in your church who have kids? Don't your kids have friends or relatives with whom they could do a monthly overnight? Maybe you could work out a co-op type thing with one or more other couples...they take the kids one night and you and your wife take their kids on another night. Everybody wins.
Like I said before...small church, small community. Believe it or not, three kids now days seems to be a big number. My pastor has 5, but dumping my kids on his lap would difinately overload him. Most of our friends have one or two kids. Unfortunately, there is no one family that all three of my kids enjoy all of there kids.
Like I said in a different response, I know it isn't impossible. I will make it a mission of mine to find someway to get all of the kids being watched by someone. Both my wife and I love our kids dearly and don't like doling them out, but maybe its time we made us a little bit higher of a priority.
Thanks for you input.