One approach would be to purchase a few more wireless systems and mic the priest, groom, bride, and musicians and singers. This, of course, would be kinda expensive and would need a mix and mixer (the person, not the thing) to go to camera(s). This would probably get the best overall sound possible, assuming the mics are of good quality and you have done all your frequency testing in advance.
Another method would be to use a wireless to send the output of church’s console to your camera. I’m not real experienced in the wedding business but I would think the brides voice would be the lowest of the three and that is where I would put another wireless, but away from anything that would cause clothing noise problems (don’t be afraid to place the mic with tape around the cleavage area or below it. A light creme, or white windscreen would help mask the mic element and may help isolate it from the clothiing. Synthetic fabrics and beads tend to cause problems with most lav mics and you will need to make a decision with each dress as to exactly where to place the mic.)
If you plan on this approach, try to use a submix from the house mix instead of the main outs. You can send the camera more of what you need and not what the house needs.
The approach you mentioned was to go to a stand alone recorder at the house console. You may have sync problems with the recorder unless it’s genlocked to camera, even if it’s another deck or digital. In that environment, you can’t really use a slate so you will have to send timecode to the camera and/or the recorder. I guess you could get an isolated mix to the deck and use it in post under the wireless sources that went to camera.
If you are shooting multicamera, you can send the cover camera (the wideshot) the house mix and the other cameras isolated sources but you still have to deal with sync issues between the cameras – but that’s another topic.