I would be leery of renting from a church, to be honest. The non-profit educational group I participate in has had issues from time to time with losing event space because a member of the church needed the space, instead. You'd think that a deposit and a written contract would hold our date, but apparently it's not if a church member decides they absolutely have to have that particular date.
It would be awful to rent space and book jobs, only to find out you don't have the use of the kitchen after all, because the church decided they have something more important.
(NOTE: I am NOT attacking the church, just the policies of some of the ones we've dealt with. Others have been wonderful and we have long-standing relationships with them. They would never think to do something like that. Guess it's a 'your mileage may vary' situation.)
You might check with little cafes or locally owned and operated eateries where they only serve breakfast and lunch. If they close down after lunch, there's a good chance they'd let you use their facilities. Worth a shot.
Either way, good luck!