Sorry, I still don't get it. "loss of sound" and "Does the paper shim muffle the sound?" I don't understand.
http://newt.phys.unsw.edu.au/jw/strings.html "The string on a musical instrument is (almost) fixed at both ends, so any vibration of the string must have nodes at each end. Now that limits the possible vibrations." Fixed length. I.E. the saddle and a nut/fret.
Point being it is fixed. With 16 to 19 lbs of force on each string, the tuner will set against the hole at the closest point in line with the string, relative to the nut. There shouldn't be any variation in the tuning of the string, once it's brought up to pitch. Unless you force the tuner around in the hole. And since it's past the vibration of the string, it should have minimal effect on the sound.
http://www.frudua.com/guitar_strings_tension.htm Note the "The portion of strings
not directly involved in vibration in red corresponds to a 15% / 30% of the total." They are talking about the portion from the saddle to the stop bar and the nut to the tuner. The thrust of the article is how the break angles affect bending strings. But you'll notice that they never vary from the point of the string vibration occurring between the saddle and the nut. (or the fret).
So it would seem to me the articles all say that the vibration of the string occurs between the two primary contact points, the saddle and the nut/fret. If there is no vibration beyond these, how much can they affect on the sound?
I'm not trying to be a smart _ss, I just don't understand how the "dead" part of the string has that much effect on the sound. My physics background is flailing at me. I know that people rave about the better stop bars, and I'm sure there is something to it. That's why some guitars have string through body fastening.
But at the end of the day, the tuner being a bit sloppy in the hole shouldn't produce any significant transmission loss.