Scott,
Concerning your number one, there is a likelihood that you are pulling string through the bridge pins from the hitch pin side. There is a lot of friction between the wire and the bridge pins and surface. It is likely that it is rare for that segment of the string to be in equilibrium with the speaking length, and that strings don't rend through the bridge pins during the process of tuning in the normal parameters of pitch change sufficiently to cause the segments to be equal in tension.
#2 I see no reason for the difference in left/middle/right in the scenario you present. You might substitute tuning right-middle-left just as an experiment to see whether the result changes.
#3 I prefer to tune pitch raises so that when I have completed a unison, all strings are at the target pitch. This gives me a more stable result, as I am able to use the ETD to confirm the stability of each string.
With larger pitch changes, I pull the left string slightly sharp (1-2¢), tune the middle string quickly to the left (aurally), then tune the right string to pitch precisely and with good stability. Now I pull the unison into focus and make sure all three strings are stable.
For pitch raises within about 25 cents, I don't find the need to do a second pass, or it is only about 5 - 10 minutes of refining unisons.
(Al Sanderson thought that the major factor in large pitch changes, leading to the need of offsets, is the plate being pulled. This is what led him to recommend tuning by half steps left to right, which has certainly shown itself to work very well. We see the principles involved in the broken string phenomenon, where the notes on either side of the broken one go significantly sharp, but go back to pitch when you have replaced the string and brought it to pitch. This is what I keep in mind while I am tuning each unison).
This method doesn't work using the offsets given by various ETDs, as those offsets would leave the piano significantly sharp. I set the offset myself, far more modestly: maybe 5% for bass (if any offset), 15-20% for plain wire.
With respect to your two pass for more than 100¢ cents, I have seen similar results, and found that often it is best to simply do the second pass straight to pitch, or just a very small offset.
Regards,
Fred Sturm
"When I smell a flower, I don't think about how it was cultivated. I like to listen to music the same way." Mompou