Like, for example, "the Mongols"; [...]

I'll give you the Mongols (and Hitler) since I find them harder to call.

The ones you pointed out from my previous comment, (European) slavery in Africa and smoking, have similar issues; what exactly is the disaster, how long is too long for a solution, and who is responsible for stopping it?

For deciding whether smoking and transatlantic slavery are counterexamples to "Adams' Law of Slow-Moving Disasters" (I'll just call it ALoSMD), the third question is irrelevant and the first question doesn't actually need a full, comprehensive answer. I can give just enough of a description of the problem to allow us to eyeball the problem's magnitude over time. If it became visibly worse during some period, that suffices to show it wasn't fixed during that period, and a complete description of the problem is not necessary. For smoking, we can just see when the rate at which people died from smoking was/is increasing; for transatlantic enslavement, we can ask how long the enslavement rate trended up.

(Why do I say the third question's irrelevant here? Because ALoSMD doesn't say anything about who fixes the problem or how it's fixed; it just says the problem gets fixed. Whether it's fixed by the people "responsible" or someone else is an issue the Law pushes aside.)

The Quakers decided slavery was immoral in 1783, founded the 'Society for Effecting the Abolition of the Slave Trade' in 1787, and twenty years later had killed the slave trade in the British Empire (with the rest of the Europe's slave trade crumbling soon after). It's tough to see how they could have been more prompt once they had invented the modern concept of abolitionism, and it's pretty odd to call out earlier Christians for not responding to something only an abolitionist would even call a disaster in the first place.

It's not clear to me why one would zero in on the Quakers specifically (since ALoSMD doesn't care about the who or the how), nor why one should only start the clock running from 1783. The slavers were hardly oblivious to what they were doing, and they (if no one else) could've acknowledged & avoided negative consequences of their actions from the beginning.

I grant it's morally anachronistic to criticize historical people for failing to meet current moral standards, but I don't believe that's relevant. If your best judgement, or my best judgement, says transatlantic slavery was a disaster, then as far as you or I are concerned, it simply was a disaster; that people from 400 years ago would disagree would merely make them wrong by our lights, and doesn't mean transatlantic slavery wasn't a disaster after all.

With smoking, the death rates are increasing but primarily in the developing world where cigarette smoking is still pretty new.

That's true.

In the US, our regulatory incentives and education have done a good job reducing the death toll and nowadays people generally know the risks when they pick up a pack (as do their insurance companies) all in just a few decades;

I'd dispute the idea that US smokers generally know the risks (most of them presumably know about the risk of lung cancer, but probably not about the risks of e.g. erectile dysfunction, or giving other people cardiovascular disease through secondhand smoke) but admittedly that's a side point.

domestically, it looks like the main disaster now is that the people who do choose to risk their health are increasingly able to externalize the cost of that decision through the government.

Another side point, but a Fermi estimate suggests otherwise. tobaccofreekids.org estimates that each year, in the US, smoking leads to $71 billion of taxpayer-funded government spending, and causes about 400,000 smokers' deaths. I handwavingly convert the latter number into dollars by multiplying it by the average years of life a smoker loses (13) and a $50,000 guesstimate for the value of a year of life, giving $260 billion. Setting the two dollar values side by side, the loss of life in itself appears to be the bigger problem.

My guess is that those developing countries with functioning governments will probably follow our example and we'll see falling rates globally pretty soon as well, but even so it's not far-fetched to say the disaster here is dealt with and theirs are separate (albeit similar) crises.

I could treat them as separate, but since CronoDAS picked out tobacco in general as a disaster, I'm inclined to look at global deaths. (And that seems like a natural thing to do. From the perspective of a dispassionate observer, why weigh the deaths of those in developing countries on a different scale? Also, if I did treat the developing world tobacco disaster as a separate problem, and if the best I could say about that separate problem were that it'd start improving "pretty soon", that'd indicate the problem is getting worse, hence not fixed.)

I still haven't addressed the second question out of your three ("how long is too long for a solution"), but since I can give it reasonable answers, I don't think it invalidates smoking and transatlantic slavery as counterexamples.

With respect to slavery, I can only repeat that its negative consequences were not subtle or accidental side effects; the slavers knew what they were doing from the start. As such, any delay in its prohibition would be "too long". Deliberately setting my house on fire would be a foreseeable disaster, and even if I subsequently called the fire brigade early enough to save most of the house, I could hardly say the disaster was averted in time!

As for smoking, I'd set the year 2000 as an upper bound for when smoking death rates should've peaked. Why 2000? Because by that point they'd started falling in developed countries, and I see no compelling reason why that couldn't have been the case worldwide. A sufficient reason why that wasn't the case worldwide is, as far as I can tell, inadequate tobacco control.

If we're going to say people haven't responded to a disaster quickly enough, actually defining said disaster the timescale and who the responders are is fairly crucial. [...] for the purposes of understanding how people tend to respond to crises it makes more sense to try to cut as closely to the issue as possible.

It is of course a good idea to do these things if we are trying to maximize our understanding of a problem and how people respond to it. But that's not what CronoDAS & I have tried to do here. We've set ourselves the less onerous task of identifying counterexamples to ALoSMD. To carry out this narrower task we need not do all you say we need to.

I may be coming off as bullet-headed here, but we really shouldn't dismiss likely counterexamples to ALoSMD prematurely. If ALoSMD is wrong — and I reckon it is — it's a good idea to underline that fact before the ALoSMD meme lodges in people's heads and makes them complacent about civilizational & existential risks.