Your test two target shows improvement. Just how much is up for grabs.
Some other things to try........
1-Put a pressure point of some sort between the end of the stock and the barrel. Might even try moving it around to see if that matters.
2-Find some fairly thin strips of lead and wrap the barrel in various spots to see if that works better than mercury.
3-Find a rubber vibration damper and try that in various positions on the barrel.