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The secondary vibrations seemed to change somewhat with charge and bullet weight variations, but not much.
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The changes are likely due to the physical effect of the bullet travelling down the bore. The reason it's mostly constant is because what you're mostly seeing is the impulse response of the barrel system. The impulse response of the barrel (the response to the actual impulse of firing) is theoretically identical from shot to shot. In practice, the amplitude of the vibrations may vary a bit, but the vibration frequencies will be essentially identical for each shot. For the same reason a piano string makes the right note no matter how hard you hit the key although a hard hit makes a louder note.
The bullet motion in the bore is another contribution to barrel movement/vibration, and one that is more variable and load dependent.
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As far as I know, methods to deal with this interest very few people and are assuredly costly.
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In the simplest analysis, if there's a situation where it seems impossible to find an accurate load for a rifle where everything else seems to be in order, one can simply cut a small amount off the end of the barrel, recrown, and try again. Altering the length will change the impulse response and perhaps create a more favorable situation.