I have a '97 840Ci...I love this car, but I wish is was a stick...Is it possible to swap the 6 speed from the 850 (or 5 series) into my car? Any thoughts?

The 850 transmission won't work but an M62 based 540 6 speed should in your case. Pedals and hydraulics from an early 850 should work.

The only problem is that everybody (including me) talks about doing this conversion but no one seems to be bragging about having done it.

There are Euro 6 speed 840s with both M60 and M62 V8s but ZERO came to the US.