I am a user of Leica M6 -AND- Nikons. I've used the FM series for many years and I now like the cheapo N80 for its small size, spotmeter, and AF (use it w/ prime lenses mostly). I use the Leicas about half the time and the Nikons about half the time, and I work on projects like the one you describe.
I have also owned non-Leica RF cameras and in my personal experince I've found the Leica rangefinders to me much more resistant to misalignment. None of my M's have ever had misaligned rf's and I travel a lot and use them professionaly. On the other hand, my Bessa T had a vertically misaligned RF from the time it was new (still focused ok, though) and the Konica Hexar RF was also misaligned vertically, and Konica could not fix it after two tries. Well maybe it was fixed when it left them but by the time I got it it was worse than when I sent it in (vibration in transt?)
I find very little difference, if any, in the way folks respond when I shoot with an M versus a Nikon F3 or FM with a prime lens, like a 35 or a 24. It's much more to do with your attitude than with the differences in noise between the cameras. And believe me, I've shot all sorts of quiet religious rituals.
Another factor to consider is the use of the long lens. Many folks use then succesfully on rangefinders but I find it hard to compose and focus within the tiny framelines. I much prefer to shoot the longer lenses on the Nikon for the reaons stated above and because you're so aware of how much (or how little) DOF you have. I often work with two M's with, say a 35 and a 50, and an FM or F3 with the 105 or 135 Nikkors (The 100mm Series E is a very nice lens too).
One well known advantage of RF's is that you can see outside the framelines - you can see a moving subject, for instance, before it comes into the frame.
I use the Leica for all the obvious reasons, but also because I'm very comfortable with it, because I've been shooting with RF cameras for many years. You can do your project, I think, very well with your Nikon equipment but of course this is a personal choice. However, you won't find much difference between the sound of an FM and a Bessa, IMO.
One final thing: I would not hestiate to get a used Leica M6. You can get them in nearly new condition now from good sellers for around $1200. The CV lenses are great. What I would NOT do is jump into an important project with a piece of equipment I could not use intuitively.
good luck