Church options

[jaomul]

While you say you can't move around, the priest is probably used to people being very "in your face" when taking the pictures (this goes for the guests as much or maybe even more than photographers). While your question is about gear and from reviews the 5d iii is superb in these low light conditions, I would be fairly sure that if you approach the priest before the event (few days before, not 10 minutes before) and explain that you wont use flash and will be very discreet and respectful with your movements, he may lift your restrictions so to speak and make your job photographing the ceremony a whole lot easier

 

[MLeeK]

Most allow you to move around as long as you are behind the last seated guest and are unnoticeable.

 

[bledererphoto]

Good stuff. I would think as long as you are not distracting, and I'm usually hanging back for most of ceremony with a long lens, they would be fine with at least lateral movement at back.