The practice of foot binding stands out for me. It originated in China as early as the 10th century, and remained commonplace up until the early 20th. Foot binding was painful and permanently disabling, and rendered women effectively housebound and wholly dependent on their husbands.

From the tiny amount I've read, it sounds like the practice was sustained for so long through some combination of (Neo-)Confucian attitudes, and its entrenched role as a marker of beauty / femininity / honour / national identity which was only really possible to escape collectively — similar to less terrible but more familiar examples of harmful beauty standards. Top-down enforcement was not entirely necessary: the Shunzhi Emperor of the Qing dynasty even tried to abolish the practice, but failed partly owing to its popular support.

The especially sad thing is how contingent its origins seem to be — upper-class women began to imitate a story about a court dancer to the emperor, who reputedly bound her feet "into the shape of a new moon". The practice took hold as a status symbol among the elite, and spread throughout China.

I would be confident in saying at least half a billion women were subjected to this. One estimate claims some 2 billion women broke and bound their feet in total.

A lot of this is going to rest on your specific moral views and the way you define the question, rather than historical factual issues, I suspect.

• The clearest examples are going to be things like genocides and wars. For example, the An Lushan Rebellion was (arguably?) responsible for the largest fraction of humanity to be killed in on event. There have been enough of these that you could fill a very respectable list.
• If you relax your definition of what constitutes an event, things like 'all murder ever' are going to qualify. But these are clearly less dense in space-time than genocides, and many people would not count them as 'an event'.
• If you accept events that are less bad per capita, but more widespread, things like the denial of education to women, which has been quite common, and could plausibly qualify.
• If you think that government acts should be judged similarly to private ones, mass taxation, conscription, imprisonment and immigration restrictions might qualify. 
• If you accept more indirect responsibility, the failure to accelerate technological development resulted in hundreds of millions of unnecessary deaths from disease.
• If you believe in a right to a competent electorate, voters supporting predictably incompetent or immoral governments could qualify.
• If you accept ex ante rather than ex post catastrophes, early nuclear testing, where there was a plausible risk the atmosphere might catch fire, could qualify, though maybe the responsibility is not widespread enough.
• If you accept victims other than adult humans, things like factory farming and abortion will qualify.
• If you assign a lot of weight to children's preferences, mandatory schooling which forces them into strict compliance for most of the day could qualify.

The Great Big Book of Horrible Things is a list of the 100 worst man-made events in history, many of which fit your definition of moral catastrophe.

Practices (rather than events) that might fit your definition include

• slavery, in its many forms
• foot binding
• bride theft
• female genital mutilation
• bride forcefeeding
• judicial torture
• headhunting
• Apartheid, and racial segregation in other countries such as the USA and Australia

It seems valuable to distinguish between long-standing practices and things that might be called historical "events." For instance, different systems of slavery would be moral catastrophes that were long-standing practices. Wars and genocides might be more like "historical events" (although some happened over rather extended periods of time). 

Some other long-standing practices that seem to qualify, depending on your moral views. 

1. Factory farming
2. Forms of (mass) incarceration (and other systems of state-sanctioned punishment)
3. Certain actions with respect to our environment and non-human life on the planet
4. Mass mistreatment of certain groups of people (e.g. societies that accept rape)

Possible "events" that seem to qualify: 

1. Setting up colonies (many instances, was usually supported by large groups of people, not just by the governments themselves)
2. Some additional categories of events that are always or often moral catastrophes: wars, genocides, any situation in which large groups of people suffered and the world could have helped more than it did (any famine, refugee crises, etc.), democides (e.g. millions of people killed under Stalin in the USSR, even setting Holodomor aside)
3. There are resources like this list of wars and anthropogenic disasters by death toll (this also provides ideas for classification)

I'm a little concerned that attempts at trying to determine what "how often moral catastrophes happen and the scale of suffering they cause" will be highly definition-dependent. E.g. if you lower your bars for criteria # 1 and 2 for what you call a moral catastrophe, you'll get more moral catastrophes. But I personally found thinking about past "moral catastrophes" and the ways in which they were justified in different societies helpful for trying to identify possibly current and future moral catastrophes, so the project does seem quite useful. 

(By the way, another possible resource for this could be the list of references in the paper linked in the post you reference--- although I haven't actually read the paper or the references, only the summary.)

(I made this a comment as it doesn't seem specific enough to be an answer, but I'm not sure that that was the right call.)

Wikipedia has a handy and terrifying list of genocides by death toll. 

Thanks for sharing this question with us. This is a very interesting idea, and it’s good that someone pursues it.

Plus, my suggestions:

1. The Better Angels of our Nature, by Steven Pinker - particularly Ch. 4, on the “Humanitarian Revolution”. This is Pinker's book I enjoyed most; I thought it'd be a bit long when I bought it, but in the end I was complaining it was too short.
2. Turchin’s Seshat database – the “Global History Database”. Btw, I guess Turchin’s mathematical approach to history may interest you, if you’re not acquainted with it yet. Besides, I notice there’s a correlation between some atrocities in White’s book and societal collapses; so perhaps you profit from checking Luke Kemp’s research. Also, if that’s what you’re looking for, studying societal collapses may provide insights for S-risk scholars on what makes unrecoverable dystopias unlikely – in the long run, they’re hard to perpetuate, depend on unstable acceptance, and face stark competition.
3. I emphasize djbinder's tip on White’s book on atrocities. First, because it’s a good reading, second it helps consider some distinctions (like Lizka did infra) between , e.g., (i) long standing moral practices (like the slave trade - which I think is the point in the post you cite), (ii) "one-shot black swan" massacres which are (usually) quickly perceived as exceptional moral catastrophes (though White shows they happen more than you realize), and (iii) the ominous death toll caused by the side-effects (such as disease and hunger - the Horsemen often ride together) of conflicts, which are usually preventable and neglected. For instance, almost everyone has heard about Rwandan genocide (there's a Hollywood movie about it), a case of (ii), but few people have heard about the millions of deaths in the Congo wars that followed it - a case of (iii).

Your definition of moral catastrophe is based on historical measurable effects. It does not take into account internal human experiences, and it does not completely represent those subtle changes of human thinking and behaviours that could be considered immoral.  I would argue that the moral catastrophe is already in small every day immoral choices that slowly creep in the mind of people and become normal patterns of thinking.

There are moral catastrophe that lead to multiple catastrophic events like the idea of race superiority that eventually leads to slavery, and the holocaust.

There are catastrophic events that are the consequence of perfectly moral habits, like the spread of pandemic due to people taking care of their sick family.

I would suggest to revise your definition of moral catastrophe as "a pattern of thinking and behaviours that are the subtle cause of repeated situation-independent suffering for a large group of people".

Under this definition, the idea that men and women have distinct roles in society can be regarded as a moral catastrophe, as it caused many women to suffer unhappy lives throughout all human history.