I think that a big part of the answer to your question is found in our attitude...of which mine is usually a problem. If we are gracious, inclusive and loving of other churches then the issue of whether they accept the partnership is not our problem. My attitude is often, "Oh, they're just dinosaurs," assume that they would not wish to help, and then do an end run around them.
It would probably be better...much better...to say, "Hey, God's called us to do this over hear and I'm wondering if you'd like to be part of the action?" If they feel threatened and refuse the offer, then I thank them for considering it and "shake the dust off my feet" and move on.
That all sounds nice and Christian, but I must confess that deep down my real thoughts are to avoid the institutional church so that its values do not contaminate the missional DNA of what people are doing as part of the Big C. Life is short, ministry opportunity is everywhere, so why go through the aggravation of trying to dialogue and disciple an institution? Seems like Jesus modeled that approach, too.