Everything I can find about the Gleissberg cycle puts it closer to 80 years, about half the period you attribute to it.

I did some quick sketches of hypothetical cycles and I can see how your original graph would have emerged from it, if the amplitudes of the 11-year cycles vary with a period somewhere near a century. I would wish to test it by extrapolating it over many centuries, preferably several millenia. If it holds up, then I might wish to contemplate some sort of causality. If it breaks down, I would conclude that the results over the past 260 years are coincidental.

Unfortunately we have no direct observations of sunspots before Galileo's time. Is there any forensic radioisotope evidence that can be attributed to past sunspot cycles with any certainty?