2nd Update:
Just returned from the range again, and after experimenting with the Limbsaver Barrel De-Resonator on a stable bolt action with less moving parts, observed that the device did not affect accuracy at all.
Rifle was my son's brand new Remington 700 SPS Stainless in 30-06 that was given for his earning of the Eagle Scout and Duty to God Awards.
Will still use the device on the Remington 30-06 autoloader which I firmly believe makes a difference due to it's multitude of moving parts.