Yes, cultural mindsets and institutions are impermanent and dynamic. But that implies they can improve as well as deteriorate.  Twelve thousand years ago most people were part of a band with a moral circle or network of three or four dozen people. Today we see networks of cooperation that involve billions in some cases.  Part of this is from the creation of rules, institutions, norms, and behavioral mindsets which allow us to increasingly solve the problems of cooperation. We have become more moral or at least our morality has become more effective and broader in scope. 

Stimulating comment!  Building upon it, perhaps it could add value if we separate human nature which we are born with and likely hasn’t changed much over the last few millennia, from human nature embedded within culture and institutions and various mindsets and frameworks.  

In other words, what do we mean by "human morality"? If we restrict it to our innate human nature, then it probably hasn’t made any progress. But if we look at our abilities to form larger and more constructive and cooperative networks, then the increase in moral progress has been immense over the last century or two. 

Two of the other major requirements for the Modern Breakthrough (McCloskey's term I believe) which I have seen in most profiles of the phenomenon (I have read dozens) have been:

1. The open nature of three plus new continents with very few people (after disease wiped them out). This not only provided 20X the room to grow in amazingly fertile areas, it also provided an influx of better staple crops (potatoes and corn), timber, and the dynamic ability to establish hundreds of new statelets.  This was both a favorable condition leading up to the IR, it also helped it reduce Malthusian constraints.  This was a one time only opportunity. 
2. Constructive competition between states. With the advents of gunpowder and cannons, Europe entered into an arms race not just toward military strength, but toward superior organizational problem solving ability. The leaders (first the Dutch, then the Brits, then Americans) were those states that were able to foster creativity and cooperation with less sclerosis and rent seeking. This led to the ascendency of representational government, freed markets with finance and corporations, and so on.  IOW, it was an arms race toward organizational effectiveness. Liberal democracies won, barely. 
    

These two forces actually self reinforced each other as did the transition to fossil fuels, machines, science and markets. 
 

If I was to try to oversimplify the Modern Breakthrough to one phrase, it was a phase transition to a higher level of network integration and coordinated problem solving.  Consider this explanation a work in progress, so to speak. 

"But if progress is a primarily matter of agency, then whether it continues is up to us."

It isn't so easy. The problem is it is not up to individual agency, but the cumulative dynamic equilibrium of 8 billion people along with a healthy dose of luck and contingency. I strongly agree that we saw unprecedented amounts of progress over the past two centuries, but there is no guarantee it will continue. 
 

That said, there are things we can do to increase the likelihood of progress. These include better understanding how progress works, and by spreading out our bets so that all our eggs aren’t in one or two baskets. 

Chris, you seem to be reducing "progress" down to "technology". This is exactly the type of thing progress studies needs to clarify. As someone who has spent half his life studying progress, my two cents on the issue is that it is helpful to view two distinct types of progress. 
The first is what I call type 1 progress or progress in capability, knowledge or technology. This is nukes! Progress in technology and capability are fairly commonplace in history and even evolution.

The second is what I call type 2 progress, or progress in outcome or welfare. This is the hard one, and is extremely rare on a population level. The first and only known example of type 2 progress in the observable universe has been with humanity over the past 250 years or so.  
 

Technology and science certainly play a crucial role in type 2 progress. But they are in no way sufficient.