O -
I would actually like to see a quantification of these 'disasters' not just in the marked/selected years, but across the intervening years as well.
It should certainly be limited to purely natural disasters, so as to eliminate any chance of coincidence between human interaction & machines (like a plane crash or a fire in a city)
It should assign a numerical value to a natural disaster based on the surface area affected and not on the population it affects. Population is too ephemeral a variable across the span of time of a single century, much less a millennium.

Essentially I'm saying you should eliminate any human variables in disasters when you quantify them, rather like pretending we humans weren't even here.

Once the scale of the disaster is quantified, the catastrophic nature of a given year can be found by simply adding each disasters quantification together.

This allows the comparison of one year to another, or even a decade to another. Thus, if these years you've picked were truly catastrophic, their totals should be rather significantly higher than any surrounding years.

Your only real limitation in this comparison will be the duration of recorded history. You can't track the bottleneck events of ~70kya and ~45kya or mega-asteroid impact events of the distant past, but you can track at least 2-500 years worth of our own record history. A single century would at least give some solid credence in numbers, but I'd recommend 2 at a minimum... far enough back to include the year without a summer, 1812.

If you do take up this research challenge, you should be sure to list references from which you pulled catastrophes, your assigned scale value (and the reasoning for that scale), and be prepared to add additional natural disasters that others may point out you are missing.

Frankly, such a centralized list would be an invaluable resource that anyone could use. If you divorced it from your theory first, you could then show it in support of your theory... but if you combine that list with your theory, then both will get dismissed.

if you quest for truth, then define it in a very rigorous fashion without postulation, theory or speculation. Once you've defined the data rigorously, then you can build a theory. Without that separate and rigorous data set, your theory isn't even a theory - it's flight of fancy and cannot be taken seriously (no offense intended)

If you quest for truth, you must first question everything you know and then question everything else after you've gotten the first answers.