Theoretically it would be possible to generate on high energetic and regular pulsed signal out of interference of waves(after all this is the principle of a femto-second laser-pulse), but the problem is that in your cosmic ray example the sources of the radition are not fixed for several years. Supernovae are to short-lived to create a constant radiation that is high enough to create such a regular high-energetic pulse. Also relativistic nuclei have a very short wavelength(should be something a lot less than 10⁻¹⁶ m) making it a lot harder(and therefor much less likely) to generate a pulsed signal of a year-long frequency.
So I would say only "earth experience increase cosmic wave activity because of solar minimums" can be right.

About the form of the beads:
Yes rotation will lead to such a shape, but that doesn't imply that every such shape origins in rotation.
Consider the following situation: two perfectly round beads come out of some volcano. During the flight they start cooling down just above their melting point. What if the beads meet on the ground? Trying to reduce surface tension they will try to merge. But they are rather cold and may not merge fast enough compared to the time needed to cool their surface below melting point. Therefor they might end up getting solid in a halfly-merged state. Such a state would look like the beads in the picture, right?

causing massive destruction

I don't think so. I would say these strikes are rather weak. Otherwise we wouldn't have such a rich environment and we should find some evidence concerning these eruptions in stone-age art.

Do you got a reliable source of the dating of the samples?

Why would the sun spit out heavier elements(like oxygen and silicon which are contained in glass) instead of lighter elements like hydrogen and helium, as those should be closer to the surface because they are lighter?