Longpath:
In part, you wrote ther following, which caught my eye, and prodded memories of things long past.
Nobody has yet mentioned that the sniper, prior to taking his 970 yard shot, attatched his scope to the mounts on his take-down rifle, put the action into the stock, and then assumed that it would actually still shoot to point of aim. Perhaps a take-down rifle could hit a man at the original 650 yds, but not a man's head at that distance, more less 970.
Back when I used to shoot National Match Course at Quantico, one day the bolt stop on my Model 70 Winchester collapsed during the 300 yard rapid fire stage. I suppose that you might imagine the "fun and games" getting the bolt back into the receiver, after each shot, especially after it had flipped around and hit me on the nose.
In any case, the Marine Rifle Repair guys worked their magic, fixing the rifle for me. Of course, it had been in and out of the stock by the time I got it back, just in time to fire the 600 yard slow fire stage. Anyhow, I had 2 sighteres and 20 record shots to go. To my great surprise, the first sighter went into the 10 ring, on call. The second sighter hit the 3"dia spottrer. I ended up shooting about 194 or so, out of a possible 200, with some X ring hits.
I may have simply been lucky, or else the glass bedding was perfect, I can't say, however all the fiddleing and farting around buy the nsiper, that you mentioned, does give one pause for thought. All sorts of wondorous sytrange things happen in the movies and or on television.